Bibliography for the Pade Approximation

short

  1. The dynamics of Pade approximation
    Tourigny, Y.; Drazin, P. G.
    Nonlinearity, 2002, vol. 15, no. 3, pp. 787-806 , Ingenta.  
  2. Composed Padé-type approximation  
    Daras, Nicholas J.  
    J. Comput. Appl. Math. 134 (2001), no. 1-2, 95--112, MathSciNet.  
  3. Multivariate Padé approximation  
    Guillaume, Philippe; Huard, Alain  
    Numerical analysis in the 20th century, Vol. I, Approximation theory. J. Comput. Appl. Math. 121 (2000), no. 1-2, 197--219, MathSciNet.  
  4. Ideas from continued fraction theory extended to Padé approximation and generalized iteration  
    Lorentzen, Lisa  
    Proceedings of the International Conference on Rational Approximation, ICRA99 (Antwerp). Acta Appl. Math. 61 (2000), no. 1-3, 185--206, MathSciNet.  
  5. Perturbed Padé approximation  
    Khodier, Ahmed M. M.  
    Int. J. Comput. Math. 74 (2000), no. 2, 247--253, MathSciNet.  
  6. Multivariate orthogonal polynomials, homogeneous Padé approximants and Gaussian cubature  
    Benouahmane, Brahim; Cuyt, Annie  
    Computational methods from rational approximation theory (Wilrijk, 1999). Numer. Algorithms 24 (2000), no. 1-2, 1--15, MathSciNet.
  7. On polynomials related with Hermite-Padé approximations to the exponential function.
    Driver, Kathy A.; Temme, Nico M.
    J. Approx. Theory 95 (1998), no. 1, 101--122, MathSciNet.  
  8. The Orthogonal Polynomials and the Pade' Approximation.
    Ahmad, Faiz
    Applied mathematics and mechanics, 1998, vol. 19, no. 7, pp. 663 , Ingenta.  
  9. Problems and progress in vector Pade approximation.
    Graves-Morris, P.R.; Roberts, D.E.
    Journal of computational and applied mathematics, 1997, vol. 77, no. 1/2, pp. 173 , Ingenta.  
  10. Simultaneous Rational Approximation to Binomial Functions  
    Michael A. Bennett  
    Transactions of the American Mathematical Society, Vol. 348, No. 5. (May, 1996), pp. 1717-1738, Jstor.  
  11. On the convergence of quadrature formulas connected with multipoint Padé-type approximation  
    González-Vera, P.; Jiménez Paiz, M.; Orive, R.; López Lagomasino, G.  
    J. Math. Anal. Appl. 202 (1996), no. 3, 747--775, MathSciNet.  
  12. Convergence of Diagonal Pade Approximants for Functions Analytic Near 0  
    D. S. Lubinsky  
    Transactions of the American Mathematical Society, Vol. 347, No. 8. (Aug., 1995), pp. 3149-3157, Jstor.  
  13. A taste of Padé approximation.
    Brezinski, C.; Van Iseghem, J.
    Acta numerica, 1995, 53--103, Acta Numer., Cambridge Univ. Press, Cambridge, 1995, MathSciNet.  
  14. Approximation of Analytic Functions: A Method of Enhanced Convergence  
    Oscar P. Bruno, Fernando Reitich  
    Mathematics of Computation, Vol. 63, No. 207. (Jul., 1994), pp. 195-213, Jstor.  
  15. An introduction to Padé approximations.
    Brezinski, C.
    Curves and surfaces in geometric design (Chamonix-Mont-Blanc, 1993), 59--65, A K Peters, Wellesley, MA, 1994.
  16. Rational Approximations to the Dilogarithm  
    Masayoshi Hata  
    Transactions of the American Mathematical Society, Vol. 336, No. 1. (Mar., 1993), pp. 363-387, Jstor.  
  17. Prehistory of the Padé approximation.
    Reczek, Krzysztof
    Opuscula Math. No. 13 (1993), 13, 20, 179--182, MathSciNet.  
  18. Choosing denominators in Padé approximation. (Spanish)
    Orive Rodríguez, Ramón A.; González-Vera, Pablo; Casasús Latorre, Luis
    Rev. Acad. Canaria Cienc. 1 (1990), 125--132, MathSciNet.  
  19. Hermite-Pade approximation (basic notions and theorems).
    Paszkowski, S.
    Journal of computational and applied mathematics, 1990, vol. 32, no. 1/2, pp. 229 , Ingenta.  
  20. Error formulas for multivariate rational interpolation and Pade approximation.
    Abouir, J.; Cuyt, A.
    Journal of computational and applied mathematics, 1990, vol. 31, no. 2, pp. 233 , Ingenta.  
  21. Duality in Pade-type approximation.
    Brezinski, C.
    Journal of computational and applied mathematics, 1990, vol. 30, no. 3, pp. 351 , Ingenta.  
  22. Procedures for Estimating the Error in Pade Approximation  
    Claude Brezinski  
    Mathematics of Computation, Vol. 53, No. 188. (Oct., 1989), pp. 639-648, Jstor.   
  23. Procedures for estimating the error in Padé approximation  
    Brezinski, Claude
    Math. Comp. 53 (1989), no. 188, 639--648, MathSciNet.   
  24. On the Error in Pade Approximation: Problem 87-9 (in Solutions)  
    Seung-Jin Bang  
    SIAM Review, Vol. 30, No. 2. (Jun., 1988), pp. 319-320, Jstor.  
  25. Orthogonal functions, Padé approximation and quadrature formulas. (Spanish)
    Casasús, L.; González-Vera, P.; Pérez-Acosta, F.
    Orthogonal polynomials and their applications (Spanish) (Vigo, 1988), 71--82, Esc. Téc. Super. Ing. Ind. Vigo, Vigo, 1989, MathSciNet.
  26. On the Error in Pade Approximation: Problem 87-9 (in Problems)  
    Edward J. Allen  
    SIAM Review, Vol. 29, No. 2. (Jun., 1987), p. 299, Jstor.  
  27. A Recursive Computation Scheme for Multivariate Rational Interpolants  
    A. Cuyt  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 1. (Feb., 1987), pp. 228-239, Jstor.  
  28. Some Asymptotic Properties of Pade Approximants to e^-x  
    C. Underhill  
    Mathematics of Computation, Vol. 47, No. 175. (Jul., 1986), pp. 253-263, Jstor.  
  29. Pade Tables of a Class of Entire Functions  
    D. S. Lubinsky  
    Proceedings of the American Mathematical Society, Vol. 94, No. 3. (Jul., 1985), pp. 399-405, Jstor.  
  30. Quick Pade Approximations    
    Michael Fox   
    The Mathematical Gazette, Vol. 69, no. 447, (March, 1985), pp. 21-24.    
  31. The Gibbs phenomenon in generalized Padé approximation.
    Németh, G.; Páris, G.
    J. Math. Phys. 26 (1985), no. 6, 1175--1178, MathSciNet.  
  32. On the Continuity of the Pade Operator  
    H. Werner, L. Wuytack  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 6. (Dec., 1983), pp. 1273-1280, Jstor.  
  33. Convergence of Linear and Nonlinear Pade Approximants from Series of Orthogonal Polynomials  
    D. S. Lubinsky, A. Sidi  
    Transactions of the American Mathematical Society, Vol. 278, No. 1. (Jul., 1983), pp. 333-345, Jstor.
  34. The Quotient-Difference Algorithm and the Pade Table: An Alternative Form and a General Continued Fraction  
    J. H. McCabe  
    Mathematics of Computation, Vol. 41, No. 163. (Jul., 1983), pp. 183-197, Jstor.  
  35. On the Faber Transform and Efficient Numerical Rational Approximation  
    S. W. Ellacott  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 5. (Oct., 1983), pp. 989-1000, Jstor.  
  36. Frequency Fitting of Rational Approximations to the Exponential Function  
    A. Iserles, S. P. Norsett  
    Mathematics of Computation, Vol. 40, No. 162. (Apr., 1983), pp. 547-559, Jstor.  
  37. A comparison of some multivariate Padé approximants  
    A. Cuyt  
    SIAM J. Math. Anal., 14:195-202, 1983.  
  38. Polynomial Type Pade Approximants  
    Geza Nemeth, Magda Zimanyi  
    Mathematics of Computation, Vol. 38, No. 158. (Apr., 1982), pp. 553-565, Jstor.  
  39. Composite Exponential Approximations  
    Arieh Iserles  
    Mathematics of Computation, Vol. 38, No. 157. (Jan., 1982), pp. 99-112, Jstor.  
  40. Block Structure in the Chebyshev-Pade Table  
    K. O. Geddes  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 5. (Oct., 1981), pp. 844-861, Jstor.  
  41. On Multivalued Exponential Approximations  
    Arieh Iserles  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 3. (Jun., 1981), pp. 480-499, Jstor.  
  42. Pade Approximants, Fractional Step Methods and Navier-Stokes Discretizations  
    C. A. Hall, T. A. Porsching  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 6. (Dec., 1980), pp. 840-851, Jstor.  
  43. Recursive Algorithms for Nonnormal Pade Tables  
    A. Bultheel  
    SIAM Journal on Applied Mathematics, Vol. 39, No. 1. (Aug., 1980), pp. 106-118, Jstor.  
  44. Recursive Algorithms for the Matrix Pade Problem  
    Adhemar Bultheel  
    Mathematics of Computation, Vol. 35, No. 151. (Jul., 1980), pp. 875-892, Jstor.  
  45. On the Generalized Pade Approximations to the Exponential Function  
    Arieh Iserles  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 4. (Aug., 1979), pp. 631-636, Jstor.  
  46. Restricted Pade Approximations to the Exponential Function  
    Syvert P. Norsett  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 5. (Oct., 1978), pp. 1008-1029, Jstor.  
  47. A Property of Euclid's Algorithm and an Application to Pade Approximation  
    Robert J. McEliece, James B. Shearer  
    SIAM Journal on Applied Mathematics, Vol. 34, No. 4. (Jun., 1978), pp. 611-615, Jstor.  
  48. On the Newton-Padé approximation problem.
    Claessens, Guido
    J. Approximation Theory 22 (1978), no. 2, 150--160, MathSciNet.  
  49. Uniqueness of Pade Approximants From Series of Orthogonal Polynomials  
    Avram Sidi  
    Mathematics of Computation, Vol. 31, No. 139. (Jul., 1977), pp. 738-739, Jstor.  
  50. An Extended Pade Procedure for Constructing Global Approximations from Asymptotic Expansions: An Explication with Examples  
    P. A. Frost, E. Y. Harper  
    SIAM Review, Vol. 18, No. 1. (Jan., 1976), pp. 62-91, Jstor.  
  51. On the Pade Table of cos z  
    Arne Magnus, Jan Wynn  
    Proceedings of the American Mathematical Society, Vol. 47, No. 2. (Feb., 1975), pp. 361-367, Jstor.  
  52. On Some Aspects of the Rational Interpolation Problem  
    Luc Wuytack  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 1. (Mar., 1974), pp. 52-60, Jstor.  
  53. Upon a Convergence Result in the Theory of the Pade Table  
    P. Wynn  
    Transactions of the American Mathematical Society, Vol. 165. (Mar., 1972), pp. 239-249, Jstor.  
  54. The Pade Table and Its Relation to Certain Algorithms of Numerical Analysis  
    W. B. Gragg  
    SIAM Review, Vol. 14, No. 1. (Jan., 1972), pp. 1-62, Jstor.  
  55. Upon the Pade Table Derived from a Stieltjes Series  
    Peter Wynn  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 4. (Dec., 1968), pp. 805-834, Jstor.  
  56. Truncation Errors in Pade Approximations to Certain Functions: An Alternative Approach  
    David Elliott  
    Mathematics of Computation, Vol. 21, No. 99. (Jul., 1967), pp. 398-406, Jstor.  
  57. Pade Approximation to the Solution of the Ricatti Equation  
    Wyman Fair  
    Mathematics of Computation, Vol. 18, No. 88. (Oct., 1964), pp. 627-634, Jstor.  
  58. A Note on the Relative Merits of Pade and Maehly's Diagonal Convergents in Computing e^x  
    R. Sankar, V. Malini  
    Mathematics of Computation, Vol. 17, No. 84. (Oct., 1963), pp. 414-418, Jstor.  
  59. Prony's Method, Z-Transforms, and Pade Approximation  
    L. Weiss, R. N. McDonough  
    SIAM Review, Vol. 5, No. 2. (Apr., 1963), pp. 145-149, Jstor.  
  60. General Theorems on the Convergence of Sequences of Pade Approximants  
    H. S. Wall  
    Transactions of the American Mathematical Society, Vol. 34, No. 2. (Apr., 1932), pp. 409-416, Jstor.  
  61. On the Pade Approximants Associated with a Positive Definite Power Series  
    H. S. Wall  
    Transactions of the American Mathematical Society, Vol. 33, No. 2. (Apr., 1931), pp. 511-532, Jstor.  
  62. On the Pade Approximants Associated with the Continued Fraction and Series of Stieltjes  
    Hubert S. Wall  
    Transactions of the American Mathematical Society, Vol. 31, No. 1. (Jan., 1929), pp. 91-116, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003