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| | ==Topics List== | | ==Topics List== |
| | {| class="wikitable sortable" | | {| class="wikitable sortable" |
| − | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | + | ! Date !! Sections [Sauer 3rd ed] !! Topics !! Prerequisite Skills !! Student Learning Outcomes |
| | |- | | |- |
| | | Week.1 | | | Week.1 |
| Line 330: |
Line 330: |
| | * Convert a matrix into UHF by Householder reflectors | | * Convert a matrix into UHF by Householder reflectors |
| | | | |
| − | ==Topics List B Wiki Format ==
| |
| − | {| class="wikitable sortable"
| |
| − | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
| |
| − | |-
| |
| − | |Week 1
| |
| − | ||
| |
| − | * Section 0.2: Loss of significant digits
| |
| − | ||
| |
| − | * [[Loss of Significant Digits]]
| |
| − | ||
| |
| − | * Binary Number System
| |
| − | * Taylor's Theorem
| |
| − | ||
| |
| − | * Nested Multiplication for Evaluating Polynomials
| |
| − | * Machine Representation of Real Numbers
| |
| − | * Loss of Significant Digits in Numerical Computing
| |
| − | * Review of Taylor's Theorem
| |
| − | |-
| |
| − | |Week 1
| |
| − | ||
| |
| − | * Section 0.2: Loss of significant digits
| |
| − | ||
| |
| − | * [[Nested Multiplication]]
| |
| − | ||
| |
| − | * Binary Number System
| |
| − | * Taylor's Theorem
| |
| − | ||
| |
| − | * Nested Multiplication for Evaluating Polynomials
| |
| − | * Machine Representation of Real Numbers
| |
| − | * Loss of Significant Digits in Numerical Computing
| |
| − | * Review of Taylor's Theorem
| |
| − | |-
| |
| − | |Week 1
| |
| − | ||
| |
| − | * Section 1.1: Fixed-Point Iteration
| |
| − | ||
| |
| − | * [[Bisection Method]]
| |
| − | ||
| |
| − | * Intermediate Value Theorem
| |
| − | ||
| |
| − | * Bisection Method and Implementation
| |
| − | * Brief Introduction to Matlab
| |
| − | |-
| |
| − | |Week 2
| |
| − | ||
| |
| − | * Section 1.2: Fixed-Point Iteration
| |
| − | ||
| |
| − | * [[Fixed-Point Iteration]]
| |
| − | ||
| |
| − | * Limit of Sequences
| |
| − | * Solution Multiplicity of Equations
| |
| − | ||
| |
| − | * Geometric Interpretation of Fixed-Point Iteration
| |
| − | * Convergence of Fixed Point Iterations
| |
| − | * Order of Convergence of Iterative Methods
| |
| − | |-
| |
| − | |Week 2
| |
| − | ||
| |
| − | * Section 1.2: Fixed-Point Iteration
| |
| − | ||
| |
| − | * [[Order of Convergence of Iterative Methods]]
| |
| − | ||
| |
| − | * Limit of Sequences
| |
| − | * Solution Multiplicity of Equations
| |
| − | ||
| |
| − | * Geometric Interpretation of Fixed-Point Iteration
| |
| − | * Convergence of Fixed Point Iterations
| |
| − | * Order of Convergence of Iterative Methods
| |
| − | |-
| |
| − | |Week 2
| |
| − | ||
| |
| − | * Section 1.3: Limits of Accuracy: Conditioning of Problems
| |
| − | ||
| |
| − | * [[Wilkinson Polynomial]]
| |
| − | ||
| |
| − | * Limit of Sequences
| |
| − | * Solution Multiplicity of Equations
| |
| − | ||
| |
| − | * Sensitivity Analysis of Root-Finding
| |
| − | * Error Magnification Factor for Solution of Equations
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.4: Newton's Method
| |
| − | ||
| |
| − | * [[Newton's Method]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | * Fixed-Point Iteration
| |
| − | ||
| |
| − | * Algebraic and Geometric Interpretation of Newton's method
| |
| − | * Error Analysis for Newton's Method Based on Taylor's Theorem
| |
| − | * Newton's Method as a Fixed Point Iteration
| |
| − | * Modified Newton's Method and its Rate of Convergence
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.4: Newton's Method
| |
| − | ||
| |
| − | * [[Error Analysis for Newton's Method]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | * Fixed-Point Iteration
| |
| − | ||
| |
| − | * Algebraic and Geometric Interpretation of Newton's method
| |
| − | * Error Analysis for Newton's Method Based on Taylor's Theorem
| |
| − | * Newton's Method as a Fixed Point Iteration
| |
| − | * Modified Newton's Method and its Rate of Convergence
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.4: Newton's Method
| |
| − | ||
| |
| − | * [[Modified Newton's Method]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | * Fixed-Point Iteration
| |
| − | ||
| |
| − | * Algebraic and Geometric Interpretation of Newton's method
| |
| − | * Error Analysis for Newton's Method Based on Taylor's Theorem
| |
| − | * Newton's Method as a Fixed Point Iteration
| |
| − | * Modified Newton's Method and its Rate of Convergence
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.4: Newton's Method
| |
| − | ||
| |
| − | * [[Root-Finding Without Derivatives]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | * Fixed-Point Iteration
| |
| − | ||
| |
| − | * Algebraic and Geometric Interpretation of Newton's method
| |
| − | * Error Analysis for Newton's Method Based on Taylor's Theorem
| |
| − | * Newton's Method as a Fixed Point Iteration
| |
| − | * Modified Newton's Method and its Rate of Convergence
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.4: Newton's Method
| |
| − | ||
| |
| − | * [[Secant Method and its Convergence]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | * Fixed-Point Iteration
| |
| − | ||
| |
| − | * Algebraic and Geometric Interpretation of Newton's method
| |
| − | * Error Analysis for Newton's Method Based on Taylor's Theorem
| |
| − | * Newton's Method as a Fixed Point Iteration
| |
| − | * Modified Newton's Method and its Rate of Convergence
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.4: Newton's Method
| |
| − | ||
| |
| − | * [[Method of False Position, Muller's Method]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | * Fixed-Point Iteration
| |
| − | ||
| |
| − | * Algebraic and Geometric Interpretation of Newton's method
| |
| − | * Error Analysis for Newton's Method Based on Taylor's Theorem
| |
| − | * Newton's Method as a Fixed Point Iteration
| |
| − | * Modified Newton's Method and its Rate of Convergence
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.4: Newton's Method
| |
| − | ||
| |
| − | * [[Stopping Criteria for Iterative Methods]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | * Fixed-Point Iteration
| |
| − | ||
| |
| − | * Algebraic and Geometric Interpretation of Newton's method
| |
| − | * Error Analysis for Newton's Method Based on Taylor's Theorem
| |
| − | * Newton's Method as a Fixed Point Iteration
| |
| − | * Modified Newton's Method and its Rate of Convergence
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.5 Root-Finding Without Derivatives
| |
| − | ||
| |
| − | * [[Secant Method]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | ||
| |
| − | * Secant Method and its Convergence
| |
| − | * Stopping Criteria for Iterative Methods
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.5 Root-Finding Without Derivatives
| |
| − | ||
| |
| − | * [[Method of False Position]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | ||
| |
| − | * Secant Method and its Convergence
| |
| − | * Stopping Criteria for Iterative Methods
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.5 Root-Finding Without Derivatives
| |
| − | ||
| |
| − | * [[Muller's Method]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | ||
| |
| − | * Secant Method and its Convergence
| |
| − | * Stopping Criteria for Iterative Methods
| |
| − | |-
| |
| − | |Week 3
| |
| − | ||
| |
| − | * Section 1.5 Root-Finding Without Derivatives
| |
| − | ||
| |
| − | * [[Stopping Criteria]]
| |
| − | ||
| |
| − | * Remainder of Taylor's Series
| |
| − | * Intermediate Value Theorem
| |
| − | ||
| |
| − | * Secant Method and its Convergence
| |
| − | * Stopping Criteria for Iterative Methods
| |
| − | |-
| |
| − | |Week 4
| |
| − | ||
| |
| − | * Section 2.1 Solve Systems of Linear Equations: Gaussian Elimination
| |
| − | ||
| |
| − | * [[Gaussian Elimination]]
| |
| − | ||
| |
| − | * Elementary Row Operations
| |
| − | ||
| |
| − | * Gaussian Elimination and its Operation Counts
| |
| − | * Gaussian Elimination with Pivoting
| |
| − | * Implementation of Gauss Elimination
| |
| − | |-
| |
| − | |Week 4
| |
| − | ||
| |
| − | * Section 2.2 Solve Systems of Linear Equations: LU Decomposition
| |
| − | ||
| |
| − | * [[LU Decomposition]]
| |
| − | ||
| |
| − | * Matrix-Matrix Products
| |
| − | * Matrix-Vector Products
| |
| − | * Inverse Matrix
| |
| − | * Elementary Row Operations
| |
| − | ||
| |
| − | * Matrices for Elementary Row Operations
| |
| − | * Gauss Elimination as Matrix Products
| |
| − | * Advantages of Solutions by LU Decomposition
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.3 Error Analysis for Solution of Ax=b
| |
| − | ||
| |
| − | * [[Norms]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Various Norms for Vectors and Matrices: Compatibility of Vector and Matrix Norms
| |
| − | * Error Analysis for Solution of Ax=b
| |
| − | * Error Magnification Factor and Condition Number of Matrix
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.3 Error Analysis for Solution of Ax=b
| |
| − | ||
| |
| − | * [[Error Analysis for Solution of Ax=b]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Various Norms for Vectors and Matrices: Compatibility of Vector and Matrix Norms
| |
| − | * Error Analysis for Solution of Ax=b
| |
| − | * Error Magnification Factor and Condition Number of Matrix
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.3 Error Analysis for Solution of Ax=b
| |
| − | ||
| |
| − | * [[Error Magnification Factor and Condition Number of Matrix]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Various Norms for Vectors and Matrices: Compatibility of Vector and Matrix Norms
| |
| − | * Error Analysis for Solution of Ax=b
| |
| − | * Error Magnification Factor and Condition Number of Matrix
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.5: Iterative Methods for Solving Ax=b
| |
| − | ||
| |
| − | * [[Iterative Methods]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Convergence of General Iterative Method for Solving System of Linear Equations
| |
| − | * Comparison of Gauss Elimination and Iterative Methods
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.5: Iterative Methods for Solving Ax=b
| |
| − | ||
| |
| − | * [[Jacobi Method]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Convergence of General Iterative Method for Solving System of Linear Equations
| |
| − | * Comparison of Gauss Elimination and Iterative Methods
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.5: Iterative Methods for Solving Ax=b
| |
| − | ||
| |
| − | * [[Gauss-Seidel Method]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Convergence of General Iterative Method for Solving System of Linear Equations
| |
| − | * Comparison of Gauss Elimination and Iterative Methods
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.5: Iterative Methods for Solving Ax=b
| |
| − | ||
| |
| − | * [[Successive-Over-Relaxation (SOR) Method]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Convergence of General Iterative Method for Solving System of Linear Equations
| |
| − | * Comparison of Gauss Elimination and Iterative Methods
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.5: Iterative Methods for Solving Ax=b
| |
| − | ||
| |
| − | * [[Convergence of Iterative Methods]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Convergence of General Iterative Method for Solving System of Linear Equations
| |
| − | * Comparison of Gauss Elimination and Iterative Methods
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.5: Iterative Methods for Solving Ax=b
| |
| − | ||
| |
| − | * [[Spectral Radius of Matrix]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Convergence of General Iterative Method for Solving System of Linear Equations
| |
| − | * Comparison of Gauss Elimination and Iterative Methods
| |
| − | |-
| |
| − | |Week 5
| |
| − | ||
| |
| − | * Section 2.5: Iterative Methods for Solving Ax=b
| |
| − | ||
| |
| − | * [[Sparse Matrix]]
| |
| − | ||
| |
| − | * Length of Vectors
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Eigenvectors of a Matrix
| |
| − | ||
| |
| − | * Convergence of General Iterative Method for Solving System of Linear Equations
| |
| − | * Comparison of Gauss Elimination and Iterative Methods
| |
| − | |-
| |
| − | |Week 6
| |
| − | ||
| |
| − | * Section 2.6: Conjugate Gradient (CG) Method
| |
| − | ||
| |
| − | * [[Conjugate Gradient Method]]
| |
| − | ||
| |
| − | * Scalar Product of Vectors
| |
| − | * Determinant of a Matrix
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Quadratic Polynomials of n-variables
| |
| − | * Partial Derivatives
| |
| − | * Gradients
| |
| − | * Chain Rule for Partial Derivatives
| |
| − | ||
| |
| − | * Symmetric Positive Definite Matrix and Properties
| |
| − | * Construction of Conjugate Gradient (CG) Method
| |
| − | * Properties of CG Method
| |
| − | * Preconditioning for CG Method
| |
| − | |-
| |
| − | |Week 6
| |
| − | ||
| |
| − | * Section 2.6: Conjugate Gradient (CG) Method
| |
| − | ||
| |
| − | * [[Symmetric Positive Definite Matrix]]
| |
| − | ||
| |
| − | * Scalar Product of Vectors
| |
| − | * Determinant of a Matrix
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Quadratic Polynomials of n-variables
| |
| − | * Partial Derivatives
| |
| − | * Gradients
| |
| − | * Chain Rule for Partial Derivatives
| |
| − | ||
| |
| − | * Symmetric Positive Definite Matrix and Properties
| |
| − | * Construction of Conjugate Gradient (CG) Method
| |
| − | * Properties of CG Method
| |
| − | * Preconditioning for CG Method
| |
| − | |-
| |
| − | |Week 6
| |
| − | ||
| |
| − | * Section 2.6: Conjugate Gradient (CG) Method
| |
| − | ||
| |
| − | * [[CG Method]]
| |
| − | ||
| |
| − | * Scalar Product of Vectors
| |
| − | * Determinant of a Matrix
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Quadratic Polynomials of n-variables
| |
| − | * Partial Derivatives
| |
| − | * Gradients
| |
| − | * Chain Rule for Partial Derivatives
| |
| − | ||
| |
| − | * Symmetric Positive Definite Matrix and Properties
| |
| − | * Construction of Conjugate Gradient (CG) Method
| |
| − | * Properties of CG Method
| |
| − | * Preconditioning for CG Method
| |
| − | |-
| |
| − | |Week 6
| |
| − | ||
| |
| − | * Section 2.7: Nonlinear System of Equations
| |
| − | ||
| |
| − | * [[Nonlinear System of Equations]]
| |
| − | ||
| |
| − | * Scalar Product of Vectors
| |
| − | * Determinant of a Matrix
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Quadratic Polynomials of n-variables
| |
| − | * Partial Derivatives
| |
| − | * Gradients
| |
| − | * Chain Rule for Partial Derivatives
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 6
| |
| − | ||
| |
| − | * Section 2.7: Nonlinear System of Equations
| |
| − | ||
| |
| − | * [[Taylor's Theorem for Multi-Variate Vector Valued Functions]]
| |
| − | ||
| |
| − | * Scalar Product of Vectors
| |
| − | * Determinant of a Matrix
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Quadratic Polynomials of n-variables
| |
| − | * Partial Derivatives
| |
| − | * Gradients
| |
| − | * Chain Rule for Partial Derivatives
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 6
| |
| − | ||
| |
| − | * Section 2.7: Nonlinear System of Equations
| |
| − | ||
| |
| − | * [[Newton's Method]]
| |
| − | ||
| |
| − | * Scalar Product of Vectors
| |
| − | * Determinant of a Matrix
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Quadratic Polynomials of n-variables
| |
| − | * Partial Derivatives
| |
| − | * Gradients
| |
| − | * Chain Rule for Partial Derivatives
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 6
| |
| − | ||
| |
| − | * Section 2.7: Nonlinear System of Equations
| |
| − | ||
| |
| − | * [[Broyden's Method]]
| |
| − | ||
| |
| − | * Scalar Product of Vectors
| |
| − | * Determinant of a Matrix
| |
| − | * Eigenvalues of a Matrix
| |
| − | * Quadratic Polynomials of n-variables
| |
| − | * Partial Derivatives
| |
| − | * Gradients
| |
| − | * Chain Rule for Partial Derivatives
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | * Sections 3.1: Data and Interpolating Functions
| |
| − | ||
| |
| − | * [[Lagrange Basis Functions]]
| |
| − | ||
| |
| − | * Fundamental Theorem of Algebra
| |
| − | * Rolle's Theorem
| |
| − | ||
| |
| − | * Properties of Lagrange Basis Functions
| |
| − | * Lagrange Form of the Interpolation Polynomials
| |
| − | * Properties of Newton's Divided Differences
| |
| − | * Newton's Form of the Interpolation Polynomials
| |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | * Sections 3.1: Data and Interpolating Functions
| |
| − | ||
| |
| − | * [[Newton's Divided Differences]]
| |
| − | ||
| |
| − | * Fundamental Theorem of Algebra
| |
| − | * Rolle's Theorem
| |
| − | ||
| |
| − | * Properties of Lagrange Basis Functions
| |
| − | * Lagrange Form of the Interpolation Polynomials
| |
| − | * Properties of Newton's Divided Differences
| |
| − | * Newton's Form of the Interpolation Polynomials
| |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | * Sections 3.1: Data and Interpolating Functions
| |
| − | ||
| |
| − | * [[Properties of Newton's Divided Differences]]
| |
| − | ||
| |
| − | * Fundamental Theorem of Algebra
| |
| − | * Rolle's Theorem
| |
| − | ||
| |
| − | * Properties of Lagrange Basis Functions
| |
| − | * Lagrange Form of the Interpolation Polynomials
| |
| − | * Properties of Newton's Divided Differences
| |
| − | * Newton's Form of the Interpolation Polynomials
| |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | * Section 3.2: Interpolation Error and Runge Phenomenon
| |
| − | ||
| |
| − | * [[Interpolation Error]]
| |
| − | ||
| |
| − | * Fundamental Theorem of Algebra
| |
| − | * Rolle's Theorem
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | * Section 3.2: Interpolation Error and Runge Phenomenon
| |
| − | ||
| |
| − | * [[Interpolation Error Analysis]]
| |
| − | ||
| |
| − | * Fundamental Theorem of Algebra
| |
| − | * Rolle's Theorem
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | * Section 3.2: Interpolation Error and Runge Phenomenon
| |
| − | ||
| |
| − | * [[Runge Phenomenon]]
| |
| − | ||
| |
| − | * Fundamental Theorem of Algebra
| |
| − | * Rolle's Theorem
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | * Section 3.2: Interpolation Error and Runge Phenomenon
| |
| − | ||
| |
| − | * [[Chebyshev Polynomial]]
| |
| − | ||
| |
| − | * Fundamental Theorem of Algebra
| |
| − | * Rolle's Theorem
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 7
| |
| − | ||
| |
| − | * Section 3.2: Interpolation Error and Runge Phenomenon
| |
| − | ||
| |
| − | * [[Error Estimates for Chebyshev Interpolation]]
| |
| − | ||
| |
| − | * Fundamental Theorem of Algebra
| |
| − | * Rolle's Theorem
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 8
| |
| − | ||
| |
| − | * Section 3.4: Cubic Splines
| |
| − | ||
| |
| − | * [[Cubic Splines]]
| |
| − | ||
| |
| − | * One-Sided Limits
| |
| − | * Continuity of Functions
| |
| − | * Indefinite Integrals
| |
| − | * Extremum Values of Multivariate Quadratic Functions
| |
| − | ||
| |
| − | * Construction of Cubic Splines for Interpolation
| |
| − | * End Conditions
| |
| − | * Properties of Cubic Spline Interpolation
| |
| − | |-
| |
| − | |Week 8
| |
| − | ||
| |
| − | * Section 3.5: Bezier Curves
| |
| − | ||
| |
| − | * [[Bezier Curves]]
| |
| − | ||
| |
| − | * One-Sided Limits
| |
| − | * Continuity of Functions
| |
| − | * Indefinite Integrals
| |
| − | * Extremum Values of Multivariate Quadratic Functions
| |
| − | ||
| |
| − | * Bezier Curve and Fonts
| |
| − | |-
| |
| − | |Week 8
| |
| − | ||
| |
| − | * Section 4.1: Least Square Method
| |
| − | ||
| |
| − | * [[Least Square Method]]
| |
| − | ||
| |
| − | * One-Sided Limits
| |
| − | * Continuity of Functions
| |
| − | * Indefinite Integrals
| |
| − | * Extremum Values of Multivariate Quadratic Functions
| |
| − | ||
| |
| − | * Least Square Method for Solving Inconsistent System of Linear Equations]
| |
| − | * Basic Properties of Least Square Solutions
| |
| − | |-
| |
| − | |Week 9
| |
| − | ||
| |
| − | * Section 4.2: Mathematical Models and Data Fitting
| |
| − | ||
| |
| − | * [[Curve Fitting]]
| |
| − | ||
| |
| − | * Linear Spaces
| |
| − | * Basis Functions
| |
| − | * Product Rule for Vector Valued Multivariate Functions
| |
| − | * Chain Rule for Vector Valued Multivariate Functions
| |
| − | ||
| |
| − | * Least square method for curve fitting and statistical modeling
| |
| − | * Survey of Models: linear model, periodic model, exponential models, logistic model, etc
| |
| − | |-
| |
| − | |Week 9
| |
| − | ||
| |
| − | * Section 4.2: Mathematical Models and Data Fitting
| |
| − | ||
| |
| − | * [[Statistical Modeling]]
| |
| − | ||
| |
| − | * Linear Spaces
| |
| − | * Basis Functions
| |
| − | * Product Rule for Vector Valued Multivariate Functions
| |
| − | * Chain Rule for Vector Valued Multivariate Functions
| |
| − | ||
| |
| − | * Least square method for curve fitting and statistical modeling
| |
| − | * Survey of Models: linear model, periodic model, exponential models, logistic model, etc
| |
| − | |-
| |
| − | |Week 9
| |
| − | ||
| |
| − | * Section 4.5: Nonlinear Least Square Fitting
| |
| − | ||
| |
| − | * [[Taylor's Theorem for Vector Valued Multivariate Functions]]
| |
| − | ||
| |
| − | * Linear Spaces
| |
| − | * Basis Functions
| |
| − | * Product Rule for Vector Valued Multivariate Functions
| |
| − | * Chain Rule for Vector Valued Multivariate Functions
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 9
| |
| − | ||
| |
| − | * Section 4.5: Nonlinear Least Square Fitting
| |
| − | ||
| |
| − | * [[Gauss-Newton Method]]
| |
| − | ||
| |
| − | * Linear Spaces
| |
| − | * Basis Functions
| |
| − | * Product Rule for Vector Valued Multivariate Functions
| |
| − | * Chain Rule for Vector Valued Multivariate Functions
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 9
| |
| − | ||
| |
| − | * Section 4.5: Nonlinear Least Square Fitting
| |
| − | ||
| |
| − | * [[Levenberg-Marquardt Method]]
| |
| − | ||
| |
| − | * Linear Spaces
| |
| − | * Basis Functions
| |
| − | * Product Rule for Vector Valued Multivariate Functions
| |
| − | * Chain Rule for Vector Valued Multivariate Functions
| |
| − | ||
| |
| − | * (TBD)
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.1: Numerical Differentiation
| |
| − | ||
| |
| − | * [[Numerical Differentiation]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Finite Difference (FD) Approximations of 1st order Derivative and Their Error Analysis
| |
| − | * FD approximations of 2nd order Derivatives and Their Error Analysis
| |
| − | * Undetermined Coefficient Method for FD Approximation
| |
| − | * Extrapolation Technique for Improving the Order of Approximation
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.1: Numerical Differentiation
| |
| − | ||
| |
| − | * [[Finite Difference (FD)]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Finite Difference (FD) Approximations of 1st order Derivative and Their Error Analysis
| |
| − | * FD approximations of 2nd order Derivatives and Their Error Analysis
| |
| − | * Undetermined Coefficient Method for FD Approximation
| |
| − | * Extrapolation Technique for Improving the Order of Approximation
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.1: Numerical Differentiation
| |
| − | ||
| |
| − | * [[Undetermined Coefficient Method]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Finite Difference (FD) Approximations of 1st order Derivative and Their Error Analysis
| |
| − | * FD approximations of 2nd order Derivatives and Their Error Analysis
| |
| − | * Undetermined Coefficient Method for FD Approximation
| |
| − | * Extrapolation Technique for Improving the Order of Approximation
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.1: Numerical Differentiation
| |
| − | ||
| |
| − | * [[Extrapolation Technique]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Finite Difference (FD) Approximations of 1st order Derivative and Their Error Analysis
| |
| − | * FD approximations of 2nd order Derivatives and Their Error Analysis
| |
| − | * Undetermined Coefficient Method for FD Approximation
| |
| − | * Extrapolation Technique for Improving the Order of Approximation
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.2: Numerical Integration: Newton-Cotes Formulas
| |
| − | ||
| |
| − | * [[Newton-Cotes]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Error Analysis based on Taylor's Theorem
| |
| − | * Error Analysis based on Interpolation Errors
| |
| − | * Degree of Precision of Quadrature Rules
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.2: Numerical Integration: Newton-Cotes Formulas
| |
| − | ||
| |
| − | * [[Midpoint rule]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Error Analysis based on Taylor's Theorem
| |
| − | * Error Analysis based on Interpolation Errors
| |
| − | * Degree of Precision of Quadrature Rules
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.2: Numerical Integration: Newton-Cotes Formulas
| |
| − | ||
| |
| − | * [[Trapezoid rule]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Error Analysis based on Taylor's Theorem
| |
| − | * Error Analysis based on Interpolation Errors
| |
| − | * Degree of Precision of Quadrature Rules
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.2: Numerical Integration: Newton-Cotes Formulas
| |
| − | ||
| |
| − | * [[Simpson's rule]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Error Analysis based on Taylor's Theorem
| |
| − | * Error Analysis based on Interpolation Errors
| |
| − | * Degree of Precision of Quadrature Rules
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.2: Numerical Integration: Newton-Cotes Formulas
| |
| − | ||
| |
| − | * [[Error Analysis based on Interpolation Errors]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Error Analysis based on Taylor's Theorem
| |
| − | * Error Analysis based on Interpolation Errors
| |
| − | * Degree of Precision of Quadrature Rules
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.2: Numerical Integration: Newton-Cotes Formulas
| |
| − | ||
| |
| − | * [[Quadrature Rules]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Error Analysis based on Taylor's Theorem
| |
| − | * Error Analysis based on Interpolation Errors
| |
| − | * Degree of Precision of Quadrature Rules
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.2: Numerical Integration: Newton-Cotes Formulas
| |
| − | ||
| |
| − | * [[Composite Quadrature Rules]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Error Analysis based on Taylor's Theorem
| |
| − | * Error Analysis based on Interpolation Errors
| |
| − | * Degree of Precision of Quadrature Rules
| |
| − | |-
| |
| − | |Week 10
| |
| − | ||
| |
| − | * Section 5.3: Numerical Integration: Romberg's Technique
| |
| − | ||
| |
| − | * [[Romberg's Technique]]
| |
| − | ||
| |
| − | * Taylor's Theorem
| |
| − | * Interpolation Error Estimates
| |
| − | * Properties of Definite Integrals
| |
| − | ||
| |
| − | * Motivation, construction and implementation of Romberg's Technique.
| |
| − | |-
| |
| − | |Week 11
| |
| − | ||
| |
| − | * Section 5.4: Adaptive Numerical Integration
| |
| − | ||
| |
| − | * [[Adaptive Numerical Integration]]
| |
| − | ||
| |
| − | * Long Divisions
| |
| − | * Substitution Methods for definite integrals
| |
| − | ||
| |
| − | * How to estimate the error on a sub interval
| |
| − | * How to mark sub intervals to be further refinement?
| |
| − | |-
| |
| − | |Week 11
| |
| − | ||
| |
| − | * Section 5.4: Adaptive Numerical Integration
| |
| − | ||
| |
| − | * [[Implementation of Adaptive Numerical Integration Techniques]]
| |
| − | ||
| |
| − | * Long Divisions
| |
| − | * Substitution Methods for definite integrals
| |
| − | ||
| |
| − | * How to estimate the error on a sub interval
| |
| − | * How to mark sub intervals to be further refinement?
| |
| − | |-
| |
| − | |Week 11
| |
| − | ||
| |
| − | * Section 5.5: Gauss Quadrature Formulas
| |
| − | ||
| |
| − | * [[Gauss Quadrature Formulas]]
| |
| − | ||
| |
| − | * Long Divisions
| |
| − | * Substitution Methods for definite integrals
| |
| − | ||
| |
| − | * Motivation and difficulties with straightforward approach
| |
| − | * Legendre polynomials and their basic properties
| |
| − | * Gauss Quadrature rule based on Legendre polynomials
| |
| − | * Degree of precision of Gauss Quadrature
| |
| − | * Gauss quadrature formula on general interval and composite Gauss rules
| |
| − | |-
| |
| − | |Week 11
| |
| − | ||
| |
| − | * Section 5.5: Gauss Quadrature Formulas
| |
| − | ||
| |
| − | * [[Orthogonal Polynomials]]
| |
| − | ||
| |
| − | * Long Divisions
| |
| − | * Substitution Methods for definite integrals
| |
| − | ||
| |
| − | * Motivation and difficulties with straightforward approach
| |
| − | * Legendre polynomials and their basic properties
| |
| − | * Gauss Quadrature rule based on Legendre polynomials
| |
| − | * Degree of precision of Gauss Quadrature
| |
| − | * Gauss quadrature formula on general interval and composite Gauss rules
| |
| − | |-
| |
| − | |Week 11
| |
| − | ||
| |
| − | * Section 5.5: Gauss Quadrature Formulas
| |
| − | ||
| |
| − | * [[Legendre polynomials]]
| |
| − | ||
| |
| − | * Long Divisions
| |
| − | * Substitution Methods for definite integrals
| |
| − | ||
| |
| − | * Motivation and difficulties with straightforward approach
| |
| − | * Legendre polynomials and their basic properties
| |
| − | * Gauss Quadrature rule based on Legendre polynomials
| |
| − | * Degree of precision of Gauss Quadrature
| |
| − | * Gauss quadrature formula on general interval and composite Gauss rules
| |
| − | |-
| |
| − | |Week 11
| |
| − | ||
| |
| − | * Section 5.5: Gauss Quadrature Formulas
| |
| − | ||
| |
| − | * [[Gauss Quadrature Rule]]
| |
| − | ||
| |
| − | * Long Divisions
| |
| − | * Substitution Methods for definite integrals
| |
| − | ||
| |
| − | * Motivation and difficulties with straightforward approach
| |
| − | * Legendre polynomials and their basic properties
| |
| − | * Gauss Quadrature rule based on Legendre polynomials
| |
| − | * Degree of precision of Gauss Quadrature
| |
| − | * Gauss quadrature formula on general interval and composite Gauss rules
| |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | * Section 10.1: Discrete Fourier Transform and Fast Fourier Transform (FTT)
| |
| − | ||
| |
| − | * [[Fourier Series]]
| |
| − | ||
| |
| − | * Complex Numbers
| |
| − | * Complex Variables
| |
| − | * Integration by Parts
| |
| − | * Convergence of Sequences
| |
| − | * Convergence of Series
| |
| − | ||
| |
| − | * Matrix Form of Discrete Fourier Transform
| |
| − | * DFT and Trigonometric Interpolation
| |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | * Section 10.1: Discrete Fourier Transform and Fast Fourier Transform (FTT)
| |
| − | ||
| |
| − | * [[Discrete Fourier Transform (DFT)]]
| |
| − | ||
| |
| − | * Complex Numbers
| |
| − | * Complex Variables
| |
| − | * Integration by Parts
| |
| − | * Convergence of Sequences
| |
| − | * Convergence of Series
| |
| − | ||
| |
| − | * Matrix Form of Discrete Fourier Transform
| |
| − | * DFT and Trigonometric Interpolation
| |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | * Section 10.1: Discrete Fourier Transform and Fast Fourier Transform (FTT)
| |
| − | ||
| |
| − | * [[Inverse Discrete Fourier Transform]]
| |
| − | ||
| |
| − | * Complex Numbers
| |
| − | * Complex Variables
| |
| − | * Integration by Parts
| |
| − | * Convergence of Sequences
| |
| − | * Convergence of Series
| |
| − | ||
| |
| − | * Matrix Form of Discrete Fourier Transform
| |
| − | * DFT and Trigonometric Interpolation
| |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | * Section 10.1: Discrete Fourier Transform and Fast Fourier Transform (FTT)
| |
| − | ||
| |
| − | * [[Fast Fourier Transform (FFT)]]
| |
| − | ||
| |
| − | * Complex Numbers
| |
| − | * Complex Variables
| |
| − | * Integration by Parts
| |
| − | * Convergence of Sequences
| |
| − | * Convergence of Series
| |
| − | ||
| |
| − | * Matrix Form of Discrete Fourier Transform
| |
| − | * DFT and Trigonometric Interpolation
| |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | * Section 11.1: Discrete Cosine Transform (optional)
| |
| − | ||
| |
| − | * [[Discrete Cosine Transform]]
| |
| − | ||
| |
| − | * Complex Numbers
| |
| − | * Complex Variables
| |
| − | * Integration by Parts
| |
| − | * Convergence of Sequences
| |
| − | * Convergence of Series
| |
| − | ||
| |
| − | * DCT and Interpolation by Cosine Functions
| |
| − | * Relation between DFT and DCT
| |
| − | * Fourier Transform of 2-Dimensional Functions
| |
| − | * DCT of 2-Dimensional Functions
| |
| − | * Interpolation Theorem for 2-Dimensional DCT
| |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | * Section 11.1: Discrete Cosine Transform (optional)
| |
| − | ||
| |
| − | * [[Discrete Cosine Transform(DCT)]]
| |
| − | ||
| |
| − | * Complex Numbers
| |
| − | * Complex Variables
| |
| − | * Integration by Parts
| |
| − | * Convergence of Sequences
| |
| − | * Convergence of Series
| |
| − | ||
| |
| − | * DCT and Interpolation by Cosine Functions
| |
| − | * Relation between DFT and DCT
| |
| − | * Fourier Transform of 2-Dimensional Functions
| |
| − | * DCT of 2-Dimensional Functions
| |
| − | * Interpolation Theorem for 2-Dimensional DCT
| |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | * Section 11.2: Image Compression (optional)
| |
| − | ||
| |
| − | * [[Quantization]]
| |
| − | ||
| |
| − | * Complex Numbers
| |
| − | * Complex Variables
| |
| − | * Integration by Parts
| |
| − | * Convergence of Sequences
| |
| − | * Convergence of Series
| |
| − | ||
| |
| − | * Digital Gray scale images and color color images
| |
| − | * RGB format
| |
| − | * YCbCr (or YUV) format
| |
| − | * Convertion between RGB and YUV formats
| |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | * Section 11.2: Image Compression (optional)
| |
| − | ||
| |
| − | * [[Image Compression]]
| |
| − | ||
| |
| − | * Complex Numbers
| |
| − | * Complex Variables
| |
| − | * Integration by Parts
| |
| − | * Convergence of Sequences
| |
| − | * Convergence of Series
| |
| − | ||
| |
| − | * Digital Gray scale images and color color images
| |
| − | * RGB format
| |
| − | * YCbCr (or YUV) format
| |
| − | * Convertion between RGB and YUV formats
| |
| − | |-
| |
| − | |Week 12
| |
| − | ||
| |
| − | * Section 11.2: Image Compression (optional)
| |
| − | ||
| |
| − | * [[Image Decompression]]
| |
| − | ||
| |
| − | * Complex Numbers
| |
| − | * Complex Variables
| |
| − | * Integration by Parts
| |
| − | * Convergence of Sequences
| |
| − | * Convergence of Series
| |
| − | ||
| |
| − | * Digital Gray scale images and color color images
| |
| − | * RGB format
| |
| − | * YCbCr (or YUV) format
| |
| − | * Convertion between RGB and YUV formats
| |
| − | |-
| |
| − | |Week 13
| |
| − | ||
| |
| − | * Section 12.1: Power Iteration Methods
| |
| − | ||
| |
| − | * [[Power Iteration Methods]]
| |
| − | ||
| |
| − | * Eigenvalues
| |
| − | * Eigenvectors
| |
| − | * Orthonormal Bases and the Gram-Schmidt Process
| |
| − | ||
| |
| − | * Convergence of Power Iteration Methods
| |
| − | |-
| |
| − | |Week 13
| |
| − | ||
| |
| − | * Section 12.1: Power Iteration Methods
| |
| − | ||
| |
| − | * [[Inverse Power Iteration]]
| |
| − | ||
| |
| − | * Eigenvalues
| |
| − | * Eigenvectors
| |
| − | * Orthonormal Bases and the Gram-Schmidt Process
| |
| − | ||
| |
| − | * Convergence of Power Iteration Methods
| |
| − | |-
| |
| − | |Week 13
| |
| − | ||
| |
| − | * Section 12.1: Power Iteration Methods
| |
| − | ||
| |
| − | * [[Inverse Power Iteration with Shift]]
| |
| − | ||
| |
| − | * Eigenvalues
| |
| − | * Eigenvectors
| |
| − | * Orthonormal Bases and the Gram-Schmidt Process
| |
| − | ||
| |
| − | * Convergence of Power Iteration Methods
| |
| − | |-
| |
| − | |Week 13
| |
| − | ||
| |
| − | * Section 12.1: Power Iteration Methods
| |
| − | ||
| |
| − | * [[Rayleigh Quotient Iteration]]
| |
| − | ||
| |
| − | * Eigenvalues
| |
| − | * Eigenvectors
| |
| − | * Orthonormal Bases and the Gram-Schmidt Process
| |
| − | ||
| |
| − | * Convergence of Power Iteration Methods
| |
| − | |-
| |
| − | |Week 13
| |
| − | ||
| |
| − | * Section 12.2: QR Algorithm for Computing Eigenvalues
| |
| − | ||
| |
| − | * [[Orthogonal Matrices]]
| |
| − | ||
| |
| − | * Eigenvalues
| |
| − | * Eigenvectors
| |
| − | * Orthonormal Bases and the Gram-Schmidt Process
| |
| − | ||
| |
| − | * Definition and basic properties of orthogonal matrices
| |
| − | * QR-Factorization based on Gram-Schmidt Orthogonalization
| |
| − | |-
| |
| − | |Week 13
| |
| − | ||
| |
| − | * Section 12.2: QR Algorithm for Computing Eigenvalues
| |
| − | ||
| |
| − | * [[QR-Factorization]]
| |
| − | ||
| |
| − | * Eigenvalues
| |
| − | * Eigenvectors
| |
| − | * Orthonormal Bases and the Gram-Schmidt Process
| |
| − | ||
| |
| − | * Definition and basic properties of orthogonal matrices
| |
| − | * QR-Factorization based on Gram-Schmidt Orthogonalization
| |
| − | |-
| |
| − | |Week 13
| |
| − | ||
| |
| − | * Section 12.2: QR Algorithm for Computing Eigenvalues
| |
| − | ||
| |
| − | * [[Normalized Simultaneous Iteration(NSI)]]
| |
| − | ||
| |
| − | * Eigenvalues
| |
| − | * Eigenvectors
| |
| − | * Orthonormal Bases and the Gram-Schmidt Process
| |
| − | ||
| |
| − | * Definition and basic properties of orthogonal matrices
| |
| − | * QR-Factorization based on Gram-Schmidt Orthogonalization
| |
| − | |-
| |
| − | |Week 13
| |
| − | ||
| |
| − | * Section 12.2: QR Algorithm for Computing Eigenvalues
| |
| − | ||
| |
| − | * [[Unshifted QR Algorithm]]
| |
| − | ||
| |
| − | * Eigenvalues
| |
| − | * Eigenvectors
| |
| − | * Orthonormal Bases and the Gram-Schmidt Process
| |
| − | ||
| |
| − | * Definition and basic properties of orthogonal matrices
| |
| − | * QR-Factorization based on Gram-Schmidt Orthogonalization
| |
| − | |-
| |
| − | |Week 13
| |
| − | ||
| |
| − | * Section 12.2: QR Algorithm for Computing Eigenvalues
| |
| − | ||
| |
| − | * [[Shifted QR Algorithm]]
| |
| − | ||
| |
| − | * Eigenvalues
| |
| − | * Eigenvectors
| |
| − | * Orthonormal Bases and the Gram-Schmidt Process
| |
| − | ||
| |
| − | * Definition and basic properties of orthogonal matrices
| |
| − | * QR-Factorization based on Gram-Schmidt Orthogonalization
| |
| − | |-
| |
| − | |Week 14
| |
| − | ||
| |
| − | * Section 12.2: QR Algorithm for Computing Eigenvalues
| |
| − | ||
| |
| − | * [[Upper Hessenberg Form (UHF)]]
| |
| − | ||
| |
| − | * Matrices for Orthogonal Projection
| |
| − | * Matrices for Reflection
| |
| − | * Block Matrices
| |
| − | * Similar Matrices
| |
| − | ||
| |
| − | * Convert a matrix into UHF by Householder reflectors
| |
| − | |-
| |
| − | |Week 14
| |
| − | ||
| |
| − | * Section 12.2: QR Algorithm for Computing Eigenvalues
| |
| − | ||
| |
| − | * [[Householder Reflector]]
| |
| − | ||
| |
| − | * Matrices for Orthogonal Projection
| |
| − | * Matrices for Reflection
| |
| − | * Block Matrices
| |
| − | * Similar Matrices
| |
| − | ||
| |
| − | * Convert a matrix into UHF by Householder reflectors
| |
| | |} | | |} |
