The works of Peter Wynn
The published works of Peter Wynn are analyzed in the book C. Brezinski, M. Redivo-Zaglia Extrapolation and Rational Approximation. The Works of the Main Contributors Springer Nature, Cham, Switzerland, 2020. https://www.springer.com/us/book/9783030584177
Papers and reports
[1] P. Wynn
A note on Salzer’s method for summing certain convergent series
J. Math. and Phys., 35 (1956) 318–320.
doi:10.1017/S030500410003173X. MR 0086910. Zbl 0072.33802.
Submitted 19 July 1955.
[2] P. Wynn
On a procrustean technique for the numerical transformation of slowly convergent sequences and series
Math. Proc. Cambridge Philos. Soc., 52 (1956) 663–671.
doi:10.1017/S030500410003173X. MR 0081979. Zbl 0072.33802.
Submitted 31 October 1955.
[3] P. Wynn
On a device for computing the em(Sn) transformation
Math. Tables Aids Comput., 10 (1956) 91–96.
doi:10.1090/S0025-5718-1956-0084056-6,
doi:10.2307/2002183. MR 0084056. Zbl 0074.04601.
[4] P. Wynn
On a cubically convergent process for determining the zeros of certain functions
Math. Tables Aids Comput., 10 (1956) 97–100.
doi:10.1090/s0025-5718-1956-0081547-9,
doi:10.2307/2002184. MR 0081547. Zbl 0073.10703.
[5] P. Wynn
Central difference and other forms of the Euler transformation
Quart. J. Mech. Appl. Math., 9 (1956) 249–256.
doi:10.1093/qjmam/9.2.249. MR 0080782. Zbl 0074.29004.
Submitted 28 July 1955.
[6] P. Wynn
On the propagation of error in certain non-linear algorithms
Numer. Math., 1 (1959) 142–149.
doi:10.1007/BF01386380. MR0107988. Zbl 0087.32502.
Submitted 26 February 1959.
[7] P. Wynn
A sufficient condition for the instability of the q-d algorithm
Numer. Math., 1 (1959) 203–207.
doi:10.1007/BF01386385. MR0109426. Zbl 0096.09501.
Submitted 25 March 1959.
[8] P. Wynn
Converging factors for continued fractions
I, II, Numer. Math., 1 (1959) 272–307; 308–320.
doi:10.1007/BF01386391,
doi:10.1007/BF01386392. MR 0116158. Zbl 0092.05101.
Submitted 25 March 1959.
[9] P. Wynn
Über einen Interpolations-algorithmus und gewisse andere Formeln, die in der Theorie der Interpolation durch
rationale Funktionen bestehen
Numer. Math., 2 (1960) 151–182.
doi:10.1007/BF01386220. MR0128597. Zbl 0222.65007.
Submitted 31 July 1959.
[10] P. Wynn
The rational approximation of functions which are formally defined by a power series expansion
Math. Comp., 14 (1960) 147–186.
doi:10.2307/2003209. MR0116457. Zbl 0173.18803.
Submitted 5 November 1959.
[11] P. Wynn
Confluent forms of certain non-linear algorithms
Arch. Math., 11 (1960) 223–236.
doi:10.1007/BF01236936. MR0128068. Zbl 0096.09502.
Submitted 5 October 1959.
[12] P. Wynn
A note on a confluent form of the ε-algorithm
Arch. Math., 11 (1960) 237–240.
doi:10.1007/BF01236937. MR0128069. Zbl 0096.09601.
Submitted 27 March 1959.
[13] P. Wynn
On the tabulation of indefinite integrals
BIT, 1 (1961) 286–290.
doi:10.1007/BF01933245. Zbl 0114.07003.
[14] P. Wynn
L’ε-algoritmo e la tavola di Padé
Rend. Mat. Roma, (V) 20 (1961) 403–408.
MR0158206. Zbl 0104.34205.
[15] P. Wynn
The epsilon algorithm and operational formulas of numerical analysis
Math. Comp., 15 (1961) 151–158.
doi:10.2307/2004221. MR0158513. Zbl 0102.33205.
[16] P. Wynn
On repeated application of the epsilon algorithm
Revue française de traitement de l’information, Chiffres, 4 (1961) 19–22.
MR0149145. Zbl 0102.33301.
[17] P. Wynn
A comparison between the numerical performances of the Euler transformation and the ε-algorithm
Revue française de traitement de l’information, Chiffres, 4 (1961) 23–29.
Zbl 0102.33302.
[18] P. Wynn
The numerical transformation of slowly convergent series by methods of comparison, Part I
Revue française de traitement de l’information, Chiffres, 4 (1961) 177–210.
MR0162350. Zbl 0113.04601.
[19] P. Wynn
A sufficient condition for the instability of the ε-algorithm
Nieuw Arch. Wiskd., 9 (1961) 117–119.
MR0139252. Zbl 0154.40305.
[20] P. Wynn
A note on a method of Bradshaw for transforming slowly convergent series and continued fractions
Amer. Math. Monthly, 69 (1962) 883–889.
doi:10.2307/2311237. MR0146559. Zbl 0112.28902.
[21] P. Wynn
Upon a second confluent form the ε-algorithm
Proc. Glasgow Math. Assoc., 5 (1962) 160–165.
doi:10.1017/S2040618500034535. MR0139253. Zbl 0118.32502.
Submitted 21 July 1961.
[22] P. Wynn
Acceleration techniques for iterated vector and matrix problems
Math. Comp., 16 (1962) 301–322.
doi:10.2307/2004051. MR0145647. Zbl 0105.10302.
[23] P. Wynn
A comparison technique for the numerical transformation of slowly convergent series based on the use of rational functions
Numer. Math., 4 (1962) 8–14.
doi:10.1007/BF01386291. MR0136500. Zbl 0138.09901.
Submitted 17 July 1961.
[24] P. Wynn
Numerical efficiency profile functions
Koninkl. Nederl. Akad. Wet., 65A (1962) 118–126.
doi:10.1016/S1385-7258(62)50011-5. MR0139257. Zbl 0105.10002.
Submitted 30 September 1961.
[25] P. Wynn
The numerical efficiency of certain continued fraction expansions
IA, IB, Koninkl. Nederl. Akad. Wet., 65A (1962) 127–137; 138–148.
doi:10.1016/S1385-7258(62)50012-7,
doi:10.1016/S1385-7258(62)50013-9. MR0139254, MR0139255. Zbl 0105.10003.
Submitted 30 September 1961.
[26] P. Wynn
On a connection between two techniques for the numerical transformation of slowly convergent series
Koninkl. Nederl. Akad. Weten., 65A (1962) 149–154.
doi:10.1016/S1385-7258(62)50014-0. MR0139256. Zbl 0138.09902.
Submitted 30 September 1961.
[27] P. Wynn
Una nota su un analogo infinitesimale del q-d algoritmo
Rend. Mat. Roma, 21 (1962) 77–85.
MR0144127. Zbl 0107.28203.
Submitted 11 September 1961.
[28] P. Wynn
A note on fitting certain types of experimental data
Stat. Neerl., 16 (1962) 145–150.
doi:10.1111/j.1467-9574.1962.tb01061.x. MR0150517.
[29] P. Wynn
Note on the solution of a certain boundary-value problem
BIT, 2 (1962) 61–64.
doi:10.1007/BF02024783. MR0155445. Zbl 0105.32103.
[30] P. Wynn
An arsenal of Algol procedures for complex arithmetic
BIT, 2 (1962) 232–255.
doi:10.1007/BF01940171. MR0166945. Zbl 0113.11605.
[31] P. Wynn
The numerical transformation of slowly convergent series by methods of comparison. Part II
Revue française de traitement de l’information, Chiffres, 5 (1962) 65–88.
MR0149146. Zbl 0221.65007.
[32] P. Wynn
Acceleration technique in numerical analysis with particular reference to problems in one independent variable,
in Information Processing 1962, Proc. IFIP Congress 62, Munich, 27 August–1 September 1962
C.M. Popplewell ed., North-Holland, Amsterdam, 1963, pp. 149–156.
Zbl 0146.14201.
[33] P. Wynn
Singular rules for certain non-linear algorithms
BIT, 3 (1963) 175–195; also Report MR 59, Mathematisch Centrum, Amsterdam, 1963.
doi:10.1007/BF01939985. MR0166946. Zbl 0123.11101.
[34] P. Wynn
Note on a converging factor for a certain continued fraction
Numer. Math., 5 (1963) 332–352.
doi:10.1007/BF01385901. MR0166902. Zbl 0117.10802.
Submitted 5 February 1963.
[35] P. Wynn
On a connection between the first and the second confluent forms of the ε-algorithm
Niew. Arch. Wisk., 11 (1963) 19–21.
MR0149147. Zbl 0116.33101.
Submitted 29 October 1962.
[36] P. Wynn
Continued fractions whose coefficients obey a non-commutative law of multiplication
Arch. Rat. Mech. Anal., 12 (1963) 273–312.
doi:10.1007/BF00281229. MR0145231. Zbl 0122.30604.
Submitted 13 August 1962.
[37] P. Wynn
A numerical study of a result of Stieltjes
Revue française de traitement del’information, Chiffres, 6 (1963) 175–196.
MR0157470. Zbl 0116.09202.
[38] P. Wynn
Converging factors for the Weber parabolic cylinder function of complex argument
Proc. Kon. Nederl. Akad. Weten., IA, IB, 66 (1963) 721–736; 737–754.
doi:10.1016/S1385-7258(63)50073-0,
doi:10.1016/S1385-7258(63)50074-2. MR0158514, MR0158515. Zbl 0235.65015.
Submitted 29 June 1963.
[39] P. Wynn
Partial differential equations associated with certain non-linear algorithms
Z. Angew. Math. Phys., 15 (1964) 273–289.
doi:10.1007/BF01607018. MR0166944. Zbl 0252.65096.
Submitted 1 September 1963.
[40] P. Wynn
General purpose vector epsilon-algorithm Algol procedures
Numer. Math., 6 (1964) 22–36.
doi:10.1007/BF01386050. MR0166947. Zbl 0113.32609.
Submitted 12 July 1963.
[41] P. Wynn
On some recent developments in the theory and application of continued fractions
SIAM J. Numer. Anal., Ser. B, 1 (1964) 177–197.
doi:10.1137/0701015. MR0178269. Zbl 0143.17804.
Submitted 4 November 1963.
[42] P. Wynn
Four lectures on the numerical application of continued fractions, in Alcune Questioni di Analisi Numerica
A. Ghizzetti ed., Series: C.I.M.E. Summer Schools, vol. 35, Springer, Heidelberg, 1965, pp. 111–251.
doi:10.1007/978-3-642-11027-6_2. Zbl 0202.43904.
[43] P. Wynn
A note on programming repeated application of the epsilon-algorithm
Revue française de traitement de l’information, Chiffres, 8 (1965) 23–62; Errata, 156.
MR0181081. Zbl 0132.36903.
[44] P. Wynn
Upon systems of recursions which obtain among the quotients of the Padé table
Numer. Math., 8 (1966) 264–269.
doi:10.1007/BF02162562. MR0215499. Zbl 0163.39502.
Submitted 5 May 1965.
[45] P. Wynn
On the convergence and stability of the epsilon algorithm
SIAM J. Numer. Anal., 3 (1966) 91–122.
doi:10.1137/0703007. MR0207180. Zbl 0299.65003.
Submitted 16 September 1965.
[46] P. Wynn
Upon a conjecture concerning a method for solving linear equations, and certain other matters
MRC Technical Summary Report 626, University of Wisconsin, Madison, April 1966.
[47] P. Wynn
Complex numbers and other extensions to the Clifford algebra with an application to the theory of continued fractions
MRC Technical Summary Report 646, University of Wisconsin, Madison, May 1966.
[48] P. Wynn
Upon the diagonal sequences of the Padé table
MRC Technical Summary Report 660, University of Wisconsin, Madison, May 1966.
[49] P. Wynn
Upon an invariant associated with the epsilon algorithm
MRC Technical Summary Report 675, University of Wisconsin, Madison, July 1966.
[50] P. Wynn
On the computation of certain functions of large argument and parameter
BIT, 6 (1966) 228–259.
doi:10.1007/BF01934356. MR0203912. Zbl 0196.48301.
[51] P. Wynn
An arsenal of Algol procedures for the evaluation of continued fractions and for effecting the epsilon algorithm
Revue française de traitement de l’information, Chiffres, 9 (1966) 327–362.
MR0203963.
[52] P. Wynn
Accelerating the convergence of a monotonic sequence by a method of intercalation
MRC Technical Summary Report 674, University of Wisconsin, Madison, January 1967.
[53] P. Wynn
A general system of orthogonal polynomials
Quart. J. Math. Oxford (2), 18 (1967) 81–96.
doi:10.1093/qmath/18.1.81. MR0210963. Zbl 0185.30001.
Submitted 8 September 1966.
[54] P. Wynn
Transformations to accelerate the convergence of Fourier series, in Gertrude Blanch Anniversary Volume
B. Mond, G. Blanch eds., Wright Patterson Air Force Base, 1967, pp. 339–379; also as MRC Technical Summary Report 673, University of Wisconsin, Madison, July 1966.
MR0215553. Zbl 0242.65004.
[55] P. Wynn
A note on the convergence of certain noncommutative continued fractions
MRC Technical Summary Report 750, University of Wisconsin, Madison, May 1967.
[56] P. Wynn
Upon the Padé table derived from a Stieltjes series
SIAM J. Numer. Anal., 5 (1968) 805–834.
doi:10.1137/0705060. MR0239734. Zbl 0175.36102.
Submitted 22 March 1968, revised 5 July 1968.
[57] P. Wynn
Vector continued fractions
Linear Algebra Appl., 1 (1968) 357–395.
doi:10.1016/0024-3795(68)90015-3. MR0231848. Zbl 0164.18503.
Submitted 5 March 1968.
[58] P. Wynn
Upon the definition of an integral as the limit of a continued fraction
Arch. Rat. Mech. Anal., 28 (1968) 83–148.
doi:10.1007/BF00283861. MR0221152. Zbl 0162.37202.
Submitted 24 May 1967.
[59] P. Wynn
Zur Theorie der mit gewissen speziellen Funktionen verknüpften Padéschen Tafeln
Math. Z., 109 (1969) 66–70.
doi:10.1007/BF01135574. MR0243242. Zbl 0175.36103.
Submitted 17 April 1968.
[60] P. Wynn
Five lectures on the numerical application of continued fractions
Orientation Lecture Series 5, MRC, University of Wisconsin, Madison.
[61] P. Wynn
Upon a recursive system of flexible rings permitting involution
Report CRM-50, Centre de Recherches Mathématiques, Université de Montréal, Montréal, November 1970.
[62] P. Wynn
Upon the inverse of formal power series over certain algebra
Report CRM-53, Centre de Recherches Mathématiques, Université de Montréal, Montréal, November 1970.
[63] P. Wynn
Upon a hierarchy of epsilon arrays
Technical Report 46, Louisiana State University, New Orleans, October 1970.
[64] P. Wynn
A note on the generalised Euler transformation
The Computer Journal, 14 (1971) 437–441; Errata 15 (1972) 175.
doi:10.1093/comjnl/14.4.437. MR0321266. Zbl 0227.65002.
[65] P. Wynn
The abstract theory of the epsilon algorithm
Report CRM-74, Centre de Recherches Mathématiques, Université de Montréal, Montréal, February 1971.
[66] P. Wynn
Upon a class of functions connected with the approximate solution of operator equations
Report CRM-103, Centre de Recherches Mathématiques, Université de Montréal, Montréal, June 1971, presented at the Workshop on Padé approximants, Marseille, 1975.
[67] P. Wynn
A note upon totally monotone sequences
Report CRM-139, Centre de Recherches Mathématiques, Université de Montréal, Montréal, November 1971.
[68] P. Wynn
A transformation of series
Calcolo, 8 (1971) 255–272.
doi:10.1007/BF02575517. MR0303675. Zbl 0236.65006.
Submitted 1 September 1971.
[69] P. Wynn
Difference-differential recursions for Padé quotients
Proc. London Math. Soc., S. 3, 23 (1971) 283–300.
doi:10.1112/plms/s3-23.2.283. MR0313682. Zbl 0221.40005.
Submitted 4 May 1970.
[70] P. Wynn
Upon the generalized inverse of a formal power series with vector valued coefficients
Compo. Math. 23 (1971) 453–460.
http://www.numdam.org/item/CM_1971__23_4_453_0. MR306224. Zbl 0239.15003.
Submitted 13 January 1971.
[71] P. Wynn
Über orthonormale Polynome und ein assoziiertes Momentproblem
Math. Scand., 29 (1971) 104–112.
doi:10.7146/math.scand.a-11038. MR0308406. Zbl 0231.30037.
Submitted 27 April 1971.
[72] P. Wynn
On an extension of a result due to Pólya
J. Reine Angew. Math., 248 (1971) 127–132.
doi:10.1515/crll.1971.248.127. MR0289771. Zbl 0219.30002.
Submitted 22 November 1969.
[73] P. Wynn
Convergence acceleration by a method of intercalation
Computing, 9 (1972) 267–273.
doi:10.1007/BF02241602. MR0315861. Zbl 0248.65003.
Submitted 6 August 1971.
[74] P. Wynn
Invariants associated with the epsilon algorithm and its first confluent form
Rend. Circ. Mat. Palermo, 21 (1972) 31–41.
doi:10.1007/BF02844229. MR0346367. Zbl 0268.65076.
Submitted January 1972.
[75] P. Wynn
Hierarchies of arrays and function sequences associated with the epsilon algorithm and its first confluent form
Rend. Mat. Roma, 5, Serie VI (1972) 819–852.
MR0355405. Zbl 0278.65002.
Submitted 15 May 1972.
[76] P. Wynn
A note on a partial differential equation
Report CRM-22, Centre de Recherches Mathématiques, Université de Montréal, Montréal, 1972.
[77] P. Wynn
Sur les suites totalement monotones
C.R. Acad. Sci. Paris, 275 A (1972) 1065–1068.
MR0310480. Zbl 0251.40001.
Accepted 6 November 1972.
[78] P. Wynn
Transformation de séries à l’aide de l’ε-algorithm
C.R. Acad. Sci. Paris, 275 A (1972) 1351–1353.
MR0311068. Zbl 0257.65005.
Accepted 18 December 1972.
[79] P. Wynn
Upon a convergence result in the theory of the Padé table
Trans. Amer. Math. Soc., 165 (1972) 239–249.
doi:10.2307/1995884. MR0293106. Zbl 0236.30013.
Received 26 October 1970, revised 21 May 1971.
[80] P. Wynn
A convergence theory of some methods of integration
Report CRM-193, Centre de Recherches Mathématiques, Université de Montréal, Montréal, May 1972.
[81] P. Wynn
The partial differential equation of the Padé surface
Report CRM-197, Centre de Recherches Mathématiques, Université de Montréal, Montréal, June 1972.
[82] P. Wynn
The algebra of certain formal power series
Report CRM-216, Centre de Recherches Mathématiques, Université de Montréal, Montréal, September 1972.
[83] P. Wynn
On some extensions of Euclid’s algorithm, and some consequences thereof
Report CRM, Centre de Recherches Mathématiques, Université de Montréal, Montréal, 1972.
[84] P. Wynn
Upon some continuous prediction algorithms. I, II
Calcolo, 9 (1973) 197–234; 235–278.
doi:10.1007/BF02576490,
doi:10.1007/BF02575582. MR0362820, MR0362821. Zbl 0281.65007. Zbl 0281.65001.
Submitted 20 June 1972.
[85] P. Wynn
On the zeros of certain confluent hypergeometric functions
Proc. Amer. Math. Soc., 40 (1973) 173–183.
doi:10.2307/2038658. MR0318529. Zbl 0268.33004.
Submitted 7 July 1972, revised 26 October 1972.
[86] P. Wynn
Accélération de la convergence de séries d’opérateurs en analyse numérique
C.R. Acad. Sci. Paris, 276 A (1973) 803–806.
MR0317519. Zbl 0268.65001.
Accepted 12 March 1973.
[87] P. Wynn
On the intersection of two classes of functions
Rev. Roumaine Math. Pures Appl., 19 (1974) 949–959.
MR0390195. Zbl 0302.30011.
[88] P. Wynn
Extremal properties of Padé quotients
Acta Math. Hungar., 25 (1974) 291–298.
doi:10.1007/BF01886088. MR0352431. Zbl 0323.30043.
Submitted 14 July 1972.
[89] P. Wynn
Sur l’équation aux dérivées partielles de la surface de Padé
C.R. Acad. Sci. Paris, 278 A (1974) 847–850.
MR0341910. Zbl 0276.35015.
[90] P. Wynn
A numerical method for estimating parameters in mathematical models
Report CRM-443, Centre de Recherches Mathématiques, Université de Montréal, Montréal, August 1974.
[91] P. Wynn
Some recent developments in the theories of continued fractions and the Padé table
Rocky Mountain J. Math., 4 (1974) 297–324.
doi:10.1216/RMJ-1974-4-2-297. MR0340880. Zbl 0302.65005.
Submitted 8 February 1973.
[92] P. Wynn
How to integrate without integrating
Colloque Euromech 58, Toulon, 1975, unpublished.
[93] P. Wynn
Upon a class of functions connected with the approximate solution of operator equations
Ann. Mat. Pura Appl., 104 (1975) 1–29.
doi:10.1007/BF02417008. MR0387553. Zbl 0315.65015.
Submitted 10 October 1972.
[94] P. Wynn
Distributive rings permitting involution
Report CRM-281, Centre de Recherches Mathématiques, Université de Montréal, Montréal, 1973.
MR0506478. Zbl 0381.17001.
[95] P. Wynn
The algebra of certain formal power series
Riv. Mat. Uni. Parma, (4) 2 (1976) 155–176.
http://www.rivmat.unipr.it/fulltext/1976-2/1976-2-155.pdf. MR0447220. Zbl 0369.16002.
Submitted 28 August 1974.
[96] P. Wynn
An array of functions
Report, School of Computer Science, McGill University, Montreal, 1976.
[97] P. Wynn
A continued fraction transformation of the Euler-MacLaurin series
Report, School of Computer Science, McGill University, Montreal, 1976.
[98] P. Wynn
A convergence theory of some methods of integration
J. Reine Angew. Math., 285 (1976) 181–208.
doi:10.1515/crll.1976.285.181. MR0415119. Zbl 0326.40005.
Submitted 22 March 1974.
[99] P. Wynn
The calculus of finite differences over certain systems of numbers
Calcolo, 14 (1977) 303–341.
doi:10.1007/BF02575990. MR0503568. Zbl 0379.65005.
Submitted 30 August 1976.
[100] P. Wynn
The transformation of series by the use of Padé quotients and more general approximants
in Padé and Rational Approximation. Theory and Applications, E.B. Saff and R.S. Varga eds., Academic Press, New York, 1977, pp. 121–144.
doi:10.1016/B978-0-12-614150-4.50015-0. MR0473660. Zbl 0368.41014.
[101] P. Wynn
The evaluation of singular and highly oscillatory integrals by use of the anti-derivative
Calcolo, 15, Fasc. IV bis, (1978) 1–103; also as Report, School of Computer Science, McGill University, Montreal, 1976.
Zbl 0531.40002.
Submitted 17 July 1977.
[102] P. Wynn
The work of E.B. Christoffel on the theory of continued fractions
in E.B. Christoffel: The Influence of His Work on Mathematics and the Physical Sciences,
P.L. Butzer, F. Fehér eds., Birkhäuser Verlag, Basel, 1981, pp. 190–202.
doi:10.1007/978-3-0348-5452-8_11. MR0661065. Zbl 0476.30004.
Submitted 9 October 1979.
[103] P. Wynn
Remark upon developments in the theories of the moment problem and of quadrature, subsequent to the work of Christoffel
in E.B. Christoffel: The Influence of His Work on Mathematics and the Physical Sciences, P.L. Butzer, F. Fehér eds., Birkhäuser Verlag, Basel, 1981, pp. 731–734.
doi:10.1007/978-3-0348-5452-8_60. MR0661114. Zbl 0484.41040.
Submitted 28 April 1980.
[104] P. Wynn
The convergence of approximating fractions
Bol. Soc. Mat. Mexicana, 26 (1981) 57–71.
MR0742016. Zbl 0479.40004.
Translations
[105] A.Ya. Khintchin
Continued Fractions
Translated from Russian by Peter Wynn, P. Noordhoff N.V., Groningen, 1963.
[106] A.N. Khovanskii
The Application of Continued Fractions and Their Generalizations to Problems in Approximation Theory
Translated from Russian by Peter Wynn, P. Noordhoff N.V., Groningen, 1963.
