Peter Wynn (mathematician)

Peter Wynn
BornOctober 1, 1931
Hertford, England
DiedDecember 2017
Zacatecas, Mexico
NationalityEnglish
Alma materJohannes Gutenberg-Universität Mainz 1959
Known forEpsilon algorithm
Scientific career
FieldsMathematician
InstitutionsMathematisch Centrum Amsterdam, University of Wisconsin-Madison, Université de Montréal, McGill University
Doctoral advisorFriedrich L. Bauer

Peter Wynn (1931—2017) was an English mathematician. His main achievements concern approximation theory – in particular the theory of Padé approximants – and its application in numerical methods for improving the rate of convergence of sequences of real numbers.

Publications

  1. Wynn, P. (1956). "A note on Salzer's method for summing certain convergent series". J. Math. Phys. 35: 318–320. doi:10.1002/sapm1956351318. MR 0086910.
  2. Wynn, Peter (1956). "On a procrustean technique for the numerical transformation of slowly convergent sequences and series". Mathematical Proceedings of the Cambridge Philosophical Society. 52 (4): 663–671. Bibcode:1956PCPS...52..663W. doi:10.1017/S030500410003173X. MR 0081979. S2CID 123285425.
  3. Wynn, Peter (1956). "On a device for computing the em(Sn) transformation". Mathematical Tables and Other Aids to Computation. 10: 91–96. doi:10.2307/2002183. JSTOR 2002183. MR 0084056.
  4. Wynn, P. (1956). "On a cubically convergent process for determining the zeros of certain functions". Mathematical Tables and Other Aids to Computation. 10 (54): 97–100. doi:10.1090/s0025-5718-1956-0081547-9. MR 0081547.
  5. Wynn, P. (1956). "Central difference and other forms of the Euler transformation". Quart. J. Mech. Appl. Math. 9 (2): 249–256. doi:10.1093/qjmam/9.2.249. MR 0080782.
  6. Wynn, Peter (1959). "On the propagation of error in certain non-linear algorithms". Numerische Mathematik. 1 (1): 142–149. doi:10.1007/BF01386380. MR 0107988. S2CID 122078822.
  7. Wynn, Peter (1959). "A sufficient condition for the instability of the q-d algorithm". Numerische Mathematik. 1 (1): 203–207. doi:10.1007/BF01386385. MR 0109426. S2CID 119934500.
  8. Wynn, P. (1959). "Converging factors for continued fractions". Numerische Mathematik. 1: 272–320. doi:10.1007/BF01386385. MR 0116158. S2CID 119934500.
  9. Wynn, Peter (1960). "Über einen Interpolations-algorithmus und gewisse andere Formeln, die in der Theorie der Interpolation durch rationale Funktionen bestehen". Numerische Mathematik. 2: 151–182. doi:10.1007/BF01386220. MR 0128597. S2CID 123016266.
  10. Wynn, Peter (1960). "On the rational approximation of functions which are formally defined by a power series expansion". Mathematical Tables and Other Aids to Computation. 14 (70): 147–186. doi:10.2307/2003209. JSTOR 2003209. MR 0116457.
  11. Wynn, Peter (1960). "Confluent forms of certain non-linear algorithms". Arch. Math. 11: 233–236. doi:10.1007/BF01236936. MR 0128068. S2CID 119969464.
  12. Wynn, Peter (1960). "A note on a confluent form of the ε-algorithm". Archiv der Mathematik. 11 (1): 237. doi:10.1007/BF01236937. MR 0128069. S2CID 120767619.
  13. Wynn, Peter (1961). "On the tabulation of indefinite integrals". BIT. Nordisk Tidskift for Information-behandling. 1 (4): 286–290. doi:10.1007/BF01933245. S2CID 119660534.
  14. Wynn, Peter (1961). "L'ε-algorithmo e la tavola di Padé". Rend. Di Mat. Roma. 20: 403. MR 0158206.
  15. Wynn, Peter (1961). "The epsilon algorithm and operational formulas of numerical analysis". Mathematics of Computation. 15 (74): 151–158. doi:10.2307/2004221. JSTOR 2004221. MR 0158513.
  16. Wynn, Peter (1961). "On repeated application of the epsilon algorithm". Chiffres. 4: 19–22. MR 0149145.
  17. Wynn, Peter (1961). "The numerical transformation of slowly convergent series by methods of comparison". Chiffres. 4: 177–210. MR 0162350.
  18. Wynn, Peter (1961). "A sufficient condition for the instability of the ε-algorithm". Nieuw Arch. Wiskunde. 9 (3): 117–119. MR 0139252.
  19. Wynn, Peter (1962). "A note on a method of Bradshaw for transforming slowly convergent series and continued fractions". American Mathematical Monthly. 69 (9): 883–889. doi:10.2307/2311237. JSTOR 2311237. MR 0146559.
  20. Wynn, Peter (1962). "Upon a second confluent form the ε-algorithm". Proceedings of the Glasgow Mathematical Association. 5: 160–165. doi:10.1017/S2040618500034535. MR 0139253.
  21. Wynn, Peter (1962). "Acceleration techniques for iterated vector and matrix problems". Mathematics of Computation. 16 (79): 301–322. doi:10.2307/2004051. JSTOR 2004051. MR 0145647.
  22. Wynn, Peter (1962). "A comparison technique for the numerical transformation of slowly convergent series based on the use of rational functions". Numerische Mathematik. 4 (1): 8–14. doi:10.1007/BF01386291. MR 0136500. S2CID 122442672.
  23. Wynn, Peter (1962). "Note on the solution of a certain boundary-value problem". BIT. 2 (1): 61–64. doi:10.1007/BF02024783. MR 0155445. S2CID 121863164.
  24. Wynn, Peter (1962). "An arsenal of ALGOL procedures for complex arithmetic". BIT. 2 (4): 232–255. doi:10.1007/BF01940171. MR 0166945. S2CID 60076831.
  25. Wynn, Peter (1962). "The numerical transformation of slowly convergent series by methods of comparison. II". Chiffres. 5: 65–88. MR 0149146.
  26. Wynn, Peter (1963). "Singular rules for certain non-linear algorithms" (PDF). BIT. 3 (3): 175–195. doi:10.1007/BF01939985. S2CID 120390887.
  27. Wynn, Peter (1963). "Note on a converging factor for a certain continued fraction". Numerische Mathematik. 5 (1): 332–352. doi:10.1007/BF01385901. S2CID 118433217.
  28. Wynn, Peter (1963). "Continued fractions whose coefficients obey a non-commutative law of multiplication". Archive for Rational Mechanics and Analysis. 12 (1): 273–312. Bibcode:1963ArRMA..12..273W. doi:10.1007/BF00281229. S2CID 119950069.
  29. Wynn, Peter (1964). "Partial differential equations associated with certain non-linear algorithms". Zeitschrift für Angewandte Mathematik und Physik. 15 (3): 273–289. Bibcode:1964ZaMP...15..273W. doi:10.1007/BF01607018. S2CID 121579702.
  30. Wynn, Peter (1964). "General purpose vector-algorithm algol procedures". Numerische Mathematik. 6 (1): 22–36. doi:10.1007/BF01386050. S2CID 123954363.
  31. Wynn, Peter (1964). "On some recent developments in the theory and application of continued fractions". Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis. 1 (1): 177–197. Bibcode:1964SJNA....1..177W. doi:10.1137/0701015. JSTOR 2949774.
  32. Wynn, Peter (1965). "A note on programming repeated application of the epsilon-algorithm". Chiffres. 8: 23–62. MR 0181081.
  33. Wynn, Peter (1966). "Upon systems of recursions which obtain among the quotients of the Padé table". Numerische Mathematik. 8 (3): 264–269. doi:10.1007/BF02162562. S2CID 123789548.
  34. Wynn, Peter (1966). "On the convergence and stability of the epsilon algorithm". SIAM Journal on Numerical Analysis. 3 (1): 91–122. Bibcode:1966SJNA....3...91W. doi:10.1137/0703007.
  35. Wynn, Peter (1966). "On the computation of certain functions of large argument and parameter". BIT. 6 (3): 228–259. doi:10.1007/BF01934356. S2CID 122412699.
  36. Wynn, Peter (1967). "A general system of orthogonal polynomials". The Quarterly Journal of Mathematics. 18 (1): 81–96. Bibcode:1967QJMat..18...81W. doi:10.1093/qmath/18.1.81.
  37. Wynn, Peter (1968). "Upon the Padé table derived from a Stieltjes series". SIAM Journal on Numerical Analysis. 5 (4): 805–834. Bibcode:1968SJNA....5..805W. doi:10.1137/0705060. JSTOR 2949427.
  38. Wynn, Peter (1968). "Vector continued fractions". Linear Algebra and Its Applications. 1 (3): 357–395. doi:10.1016/0024-3795(68)90015-3.
  39. Wynn, Peter (1969). "Zur Theorie der mit gewissen speziellen Funktionen verknüpften Padéschen Tafeln". Mathematische Zeitschrift. 109 (1): 66–77. doi:10.1007/BF01135574. S2CID 121190788.
  40. Wynn, Peter (1971). "A note on the generalised Euler transformation". The Computer Journal. 14 (4): 437–441. doi:10.1093/comjnl/14.4.437.
  41. Wynn, Peter (1971). "A transformation of series". Calcolo. 8 (3): 255–272. doi:10.1007/BF02575517. S2CID 120203819.
  42. Wynn, Peter (1971). "Difference-differential recursions for Padé quotients". Proceedings of the London Mathematical Society. s3-23 (2): 283–300. doi:10.1112/plms/s3-23.2.283.
  43. Wynn, Peter (1972). "Convergence acceleration by a method of intercalation". Computing. 9 (4): 267–273. doi:10.1007/BF02241602. S2CID 44050165.
  44. Wynn, Peter (1972). "Invariants associated with the epsilon algorithm and its first confluent form". Rendiconti del Circolo Matematico di Palermo. 21 (1–2): 31–41. doi:10.1007/BF02844229. S2CID 123537335.
  45. Wynn, Peter (1973). "Upon some continuous prediction algorithms. II". Calcolo. 9 (4): 235–278. doi:10.1007/BF02575582. S2CID 121617962.
  46. Wynn, Peter (1974). "Some recent developments in the theories of continued fractions and the Padé table". Rocky Mountain Journal of Mathematics. 4 (2): 297–324. doi:10.1216/RMJ-1974-4-2-297.
  47. Wynn, Peter (1976). "The algebra of certain formal power series". Rivista di Matematica della Università di Parma. 2 (4): 155–176. MR 0447220.
  48. Wynn, Peter (1976). "A convergence theory of some methods of integration". J. Reine Angew. Math. 1976 (285): 181–208. doi:10.1515/crll.1976.285.181. MR 0415119. S2CID 116034573.
  49. Wynn, Peter (1977). "The calculus of finite differences over certain systems of numbers". Calcolo. 14 (4): 303–341. doi:10.1007/BF02575990. MR 0503568. S2CID 120710345.
  50. Wynn, Peter (1981). "The convergence of approximating fractions". Bol. Soc. Mat. Mexicana. 26 (2): 57–71. MR 0742016.
  51. Wynn, Peter (1981). "The work of E. B. Christoffel on the theory of continued fractions". In Butzer, P. L.; Fehér, F (eds.). E. B. Christoffel: The Influence of His Work on Mathematics and the Physical Sciences. Birkhäuser Verlag. ISBN 3-7643-1162-2. MR 0661065.

MathSciNet entries

Reference books

  • C. Brezinski and M. Redivo-Zaglia: "The genesis and early developments of Aitken’s process, Shanks' transformation, the epsilon algorithm, and related fixed point methods", Numer. Algorithms, vol.80 (2019) pp.11-133.
  • C. Brezinski: "Reminiscences of Peter Wynn", Numer. Algorithms, vol.80 (2019) pp.5–11.
  • C. Brezinski and M. Redivo-Zaglia: ”Extrapolation and rational interpolation, the works of the main contributors”, Springer, 2020.

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