Peter Wynn (mathematician)

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Peter Wynn
Born 1932
Fields Mathematician
Institutions Mathematisch Centrum Amsterdam, University of Wisconsin-Madison, Université de Montréal, McGill University
Alma mater Johannes Gutenberg-Universität Mainz 1959
Doctoral advisor Friedrich L. Bauer
Known for epsilon algorithm

Peter Wynn (born 1932) is a 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[edit]

  1. Wynn, P. (1956). "A note on Salzer's method for summing certain convergent series". J. Math. and Phys. 35: 318–320. 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: 663–671. doi:10.1017/S030500410003173X. MR 0081979. 
  3. Wynn, Peter (1956). "On a device for computing the em(Sn) transformation". Mathematical Tables and Aids of 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 Aids of Computation. 10: 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. 
  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 109426. 
  8. Wynn, P. (1959). "Converging factors for continued fractions". Numerische Mathematik. 1: 272–320. doi:10.1007/BF01386385. MR 00116158. 
  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. 
  10. Wynn, Peter (1960). "On the rational approximation of functions which are formally defined by a power series expansion". Mathematical Tables and Aids of 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. 
  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. 
  13. Wynn, Peter (1961). "On the tabulation of indefinite integrals". BIT. Nordisk Tidskift for information-behandling. 1: 286–290. doi:10.1007/BF01933245. 
  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. 
  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. 
  24. Wynn, Peter (1962). "An arsenal of ALGOL procedures for complex arithmetic". BIT. 2 (4): 232–255. doi:10.1007/BF01940171. MR 0166945. 
  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. 
  27. Wynn, Peter (1963). "Note on a converging factor for a certain continued fraction". Numerische Mathematik. 5 (1): 332–352. doi:10.1007/BF01385901. 
  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. doi:10.1007/BF00281229. 
  29. Wynn, Peter (1964). "Partial differential equations associated with certain non-linear algorithms". Zeitschrift für Angewandte Mathematik und Physik. 15 (3): 273–289. doi:10.1007/BF01607018. 
  30. Wynn, Peter (1964). "General purpose vector-algorithm algol procedures". Numerische Mathematik. 6 (1): 22–36. doi:10.1007/BF01386050. 
  31. Wynn, Peter (1964). "On some recent developments in the theory and application of continued fractions". J. SIAM: Series B, Numerical Analysis. 1: 177–197. 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. 
  34. Wynn, Peter (1966). "On the convergence and stability of the epsilon algorithm". SIAM Journal on Numerical Analysis. 3 (1): 91–122. 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. 
  36. Wynn, Peter (1967). "A general system of orthogonal polynomials". The Quarterly Journal of Mathematics. 18 (1): 81–96. 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. 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. 
  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. 
  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. 
  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. 
  45. Wynn, Peter (1973). "Upon some continuous prediction algorithms. II". Calcolo. 9 (4): 235–278. doi:10.1007/BF02575582. 
  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. Mathem. 285: 181–108. doi:10.1515/crll.1976.285.181. MR 0415119. 
  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. 
  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. 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

External links[edit]