Bibliography for the Pade Approximation

unabridged

  1. The dynamics of Pade approximation
    Tourigny, Y.; Drazin, P. G.
    Nonlinearity, 2002, vol. 15, no. 3, pp. 787-806 , Ingenta.  
  2. Biorthogonal vector sequence transformations and Pade approximation of vector series
    Brezinski, C.
    Applied Numerical Mathematics, 2002, vol. 41, no. 4, pp. 437-442 , Ingenta.  
  3. Finite element analysis of two-dimensional EM scattering via Pade approximation for complex permittivity
    Abu-Zaid, N. A.; Tosun, H.
    Radio Science, 2002, vol. 37, no. 1, pp. 12-1-12-5 , Ingenta.  
  4. Pade Approximation for Extended Boundary Condition Method in Electromagnetic Scattering Analysis
    Abu-Zaid, N. A.; Tosun, H.
    Microwave and Optical Technology Letters, 2002, vol. 32, no. 2, pp. 100-101 , Ingenta.  
  5. Three-point finite-difference schemes, Padé and the spectral Galerkin method. I. One-sided impedance approximation
    Druskin, Vladimir; Moskow, Shari
    Math. Comp. 71 (2002), no. 239, 995--1019 (electronic), MathSciNet.  
  6. Composed Padé-type approximation  
    Daras, Nicholas J.  
    J. Comput. Appl. Math. 134 (2001), no. 1-2, 95--112, MathSciNet.  
  7. Analysis of high-speed interconnects using efficient multipoint Pade approximation
    Li, L. Y.; Bridges, G. E.; Ciric, I. R.
    Electronics Letters- IEE, 2001, vol. 37, no. 14, pp. 874 , Ingenta.  
  8. Padé and Padé-type approximation for 2π-periodic Lp functions  
    Daras, Nicholas J.  
    Acta Appl. Math. 62 (2000), no. 3, 245--343, MathSciNet.  
  9. 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.  
  10. 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.  
  11. Diophantine approximations using Padé approximations  
    Prévost, M.  
    Numerical analysis 2000, Vol. II: Interpolation and extrapolation. J. Comput. Appl. Math. 122 (2000), no. 1-2, 231--250, MathSciNet.  
  12. Continuity of approximation by least-squares multivariate Padé approximants  
    Huard, Alain; Robin, Vincent
    Proceedings of the 8th International Congress on Computational and Applied Mathematics, ICCAM-98 (Leuven). J. Comput. Appl. Math. 115 (2000), no. 1-2, 255--268, MathSciNet.  
  13. Perturbed Padé approximation  
    Khodier, Ahmed M. M.  
    Int. J. Comput. Math. 74 (2000), no. 2, 247--253, MathSciNet.  
  14. Conditioning and Pade Approximation of the Logarithm of a Matrix.
    Dieci, Luca; Papini, Alessandra
    Siam Journal on Matrix Analysis and Applications, 2000, vol. 21, no. 3, pp. 913 , Ingenta.  
  15. 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.
  16. Multipoint Padé-type approximation: an algebraic approach  
    González-Vera, P.; Jiménez Paiz, M.  
    Rocky Mountain J. Math. 29 (1999), no. 2, 531--558, MathSciNet.  
  17. Avoiding look-ahead in the Lanczos method and Padé approximation  
    Ayachour, E. H.  
    Appl. Math. (Warsaw) 26 (1999), no. 1, 33--62, MathSciNet.  
  18. A new Padé approximation algorithm for matrix exponentials. (Chinese)
    Gu, Chuan Qing
    Acta Automat. Sinica 25 (1999), no. 1,94--99, MathSciNet.  
  19. Error estimates in Padé approximation.
    Brezinski, C.
    Error control and adaptivity in scientific computing (Antalya, 1998), 75--85, NATO Sci. Ser. C Math. Phys. Sci., 536, Kluwer Acad. Publ., Dordrecht, 1999, MathSciNet.  
  20. A Robust Algorithm for the Solution of Electromagnetic Problems over a Frequency Interval via the Pade Approximation.
    Kuzuoglu, M.; Mittra, R.
    Microwave and optical technology letters, 1999, vol. 20, no. 6, pp. 376 , Ingenta.  
  21. Analytical approximation and Pade approximants for Volterra's population model.
    Wazwaz, A.-M.
    Applied mathematics and computation, 1999, vol. 100, no. 1, pp. 13 , Ingenta.  
  22. Relation between Padé approximations and continued fractions of generalised Laguerre functions  
    Pandey, V. K.; Lal, D. S  
    Nepali Math. Sci. Rep. 17 (1998), no. 1-2, 103--113, MathSciNet.  
  23. 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.  
  24. Spurious poles in Padé approximation.
    Stahl, Herbert
    Proceedings of the VIIIth Symposium on Orthogonal Polynomials and Their Applications (Seville, 1997). J. Comput. Appl. Math. 99 (1998), no. 1-2, 511--527, MathSciNet.  
  25. Legendre-tau-Padé approximations to the one-dimensional wave equation with boundary oscillators  
    Ito, Kazufumi; Propst, Georg  
    Numer. Funct. Anal. Optim. 19 (1998), no. 1-2, 57--70, MathSciNet.  
  26. The Orthogonal Polynomials and the Pade' Approximation.
    Ahmad, Faiz
    Applied mathematics and mechanics, 1998, vol. 19, no. 7, pp. 663 , Ingenta.  
  27. Pade Approximation and Generalization Moments.
    Chip, M.M.
    Journal of mathematical sciences., 1998, vol. 90, no. 5, pp. 2416 , Ingenta.  
  28. Parallel computing for Padé approximations of one-dimensional partial parabolic equations. (Chinese)
    Li, Hong Yun; Sheng, Wei Ping
    J. Shanghai Jiaotong Univ. (Chin. Ed.) 32 (1998), no. 8, 77--80, MathSciNet.  
  29. Padé approximation with Nourein's formula. (Japanese)
    Shiihara, Kosuke
    Trans. Inform. Process. Soc. Japan 39 (1998), no. 7, 2043--2048, MathSciNet.  
  30. A de Montessus theorem for multivariate homogeneous Padé approximants  
    A. Cuyt and D. Lubinsky  
    Ann. Numerical Mathematics, 4:217-228, 1997.  
  31. Padé approximation to an interfacial fluid mixing problem  
    Zhang, Q.; Sohn, S.-I.  
    Appl. Math. Lett. 10 (1997), no. 5, 121--127, MathSciNet.  
  32. Matrix Padé approximation of rational functions  
    Pestano-Gabino, Celina; González-Concepción, Concepción  
    Numer. Algorithms 15 (1997), no. 2, 167--192, MathSciNet.  
  33. Pade approximation for the polynomial representation of the correlation energy density functional.
    Lopez-Boada, R.; Karasiev, V.; Liu, S.
    Chemical physics letters, 1997, vol. 270, no. 5/6, pp. 443 , Ingenta.  
  34. 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.  
  35. Some properties of biorthogonal polynomials and their application to Padé approximations  
    Golub, A. P.  
    Ukrainian Math. J. 46 (1994), no. 8, 1070--1078 (1996); translated from Ukraïn. Mat. Zh. 46 (1994), no. 8, 977--984 (Russian), MathSciNet.  
  36. Radiative transfer single-scattering albedo estimation with a super-Padé approximation of Chandrasekhar's H-function  
    Steinfelds, Eric; Samuel, Mark A.; McCormick, N. J.; Reid, James H.  
    Internat. J. Theoret. Phys. 36 (1997), no. 4, 997--1007, MathSciNet.  
  37. 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.  
  38. Padé approximation of vector functions.
    Sadaka, R.
    Appl. Numer. Math. 21 (1996), no. 1, 57--70, MathSciNet.  
  39. Kronecker type theorems, normality and continuity of the multivariate Padé operator   
    A. Cuyt, K. Driver, and D. Lubinsky  
    Numer. Math., 73:311-327, 1996.  
  40. The Padé approximation of a class of entire functions. (Chinese)  
    Li, Jia Liang  
    Acta Math. Sci. (Chinese) 16 (1996), no. 1, 9--14, MathSciNet.  
  41. 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.  
  42. 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.  
  43. A taste of Padé approximation.
    Brezinski, C.; Van Iseghem, J.
    Acta numerica, 1995, 53--103, Acta Numer., Cambridge Univ. Press, Cambridge, 1995, MathSciNet.  
  44. Approximation by repeated Pade approximants.
    Ambroladze, A.; Wallin, H.
    Journal of computational and applied mathematics, 1995, vol. 62, no. 3, pp. 353 , Ingenta.  
  45. Pade Approximation for Stochastic Discrete-Event Systems.
    Gong, W. -B.; Nananukul, S.; Yan, A.
    Ieee transactions on automatic control, 1995, vol. 40, no. 8, pp. 1349 , Ingenta.  
  46. 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.  
  47. Pade-like approximation and maximum entropy formalism applied to chaotic systems.
    Steeb, W.-H.; Stoop, r.
    Journal of mathematical physics, 1994, vol. 35, no. 12, pp. 6604 , Ingenta.  
  48. Hermite-Pade approximation for Nikishin systems of analytic functions.
    Bustamante, Zh.; Lagomasino, G. Lopes
    Sbornik. Mathematics / Russian Academy of Sciences, 1994, vol. 77, no. 2, pp. 367 , Ingenta.  
  49. 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.
  50. Rational Approximations to the Dilogarithm  
    Masayoshi Hata  
    Transactions of the American Mathematical Society, Vol. 336, No. 1. (Mar., 1993), pp. 363-387, Jstor.  
  51. On convergence of Padé's approximation.
    Petkovi'c, Dojv cin
    Filomat No. 7 (1993), 73--76, MathSciNet.  
  52. Prehistory of the Padé approximation.
    Reczek, Krzysztof
    Opuscula Math. No. 13 (1993), 13, 20, 179--182, MathSciNet.  
  53. A theoretical basis for Padé approximation.
    Fitzpatrick, Patrick
    Irish Math. Soc. Bull. No. 30 (1993), 6--17, MathSciNet.  
  54. The Need for Knowledge and Reliability in Numeric Computation: Case Study of Multivariate Pade Approximation.
    Cuyt, Annie; Verdonk, Brigitte
    Acta applicandae mathematicae, 1993, vol. 33, no. 2/3, pp. 273-302 , Ingenta.  
  55. Efficient computation of the matrix exponential using Pade approximation.
    Lin, Yung-Ya; Hwang, Lian-Pin
    Computers & chemistry, 1992, vol. 16, no. 4, pp. 285 , Ingenta.  
  56. Pade Approximation and its Application in Time Series Analysis.
    Kumar, Kuldeep
    Applied mathematics and computation, 1992, vol. 48, no. 2/3, pp. 139 , Ingenta.  
  57. Error estimate in vector Pade approximation.
    Belantari, A.
    Applied numerical mathematics, 1991, vol. 8, no. 6, pp. 457 , Ingenta.  
  58. 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.  
  59. Hermite-Pade approximation (basic notions and theorems).
    Paszkowski, S.
    Journal of computational and applied mathematics, 1990, vol. 32, no. 1/2, pp. 229 , Ingenta.  
  60. Minimal vector Pade approximation.
    Bultheel, A.; Van Barel, M.
    Journal of computational and applied mathematics, 1990, vol. 32, no. 1/2, pp. 27 , Ingenta.  
  61. 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.  
  62. Duality in Pade-type approximation.
    Brezinski, C.
    Journal of computational and applied mathematics, 1990, vol. 30, no. 3, pp. 351 , Ingenta.  
  63. Procedures for Estimating the Error in Pade Approximation  
    Claude Brezinski  
    Mathematics of Computation, Vol. 53, No. 188. (Oct., 1989), pp. 639-648, Jstor.   
  64. Procedures for estimating the error in Padé approximation  
    Brezinski, Claude
    Math. Comp. 53 (1989), no. 188, 639--648, MathSciNet.   
  65. Pade Approximation of Lie Transformations in Non-linear Response-Speed Problems.
    Vishnevskiy, V.Ye.
    Soviet journal of automation and information sciences, 1989, vol. 22, no. 6, pp. 22 , Ingenta.  
  66. 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.  
  67. 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.
  68. 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.  
  69. 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.  
  70. Some Asymptotic Properties of Pade Approximants to e^-x  
    C. Underhill  
    Mathematics of Computation, Vol. 47, No. 175. (Jul., 1986), pp. 253-263, Jstor.  
  71. 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.  
  72. Quick Pade Approximations    
    Michael Fox   
    The Mathematical Gazette, Vol. 69, no. 447, (March, 1985), pp. 21-24.    
  73. The Gibbs phenomenon in generalized Padé approximation.
    Németh, G.; Páris, G.
    J. Math. Phys. 26 (1985), no. 6, 1175--1178, MathSciNet.  
  74. 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.  
  75. 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.
  76. 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.  
  77. 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.  
  78. 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.  
  79. A comparison of some multivariate Padé approximants  
    A. Cuyt  
    SIAM J. Math. Anal., 14:195-202, 1983.  
  80. An Two extensions of Padé approximation of order 1+r and their geometric interpretation. (Chinese)
    Xiao, Yin
    Dongbei Shida Xuebao 1983, no. 4, 55--59, MathSciNet.  
  81. Polynomial Type Pade Approximants  
    Geza Nemeth, Magda Zimanyi  
    Mathematics of Computation, Vol. 38, No. 158. (Apr., 1982), pp. 553-565, Jstor.  
  82. Composite Exponential Approximations  
    Arieh Iserles  
    Mathematics of Computation, Vol. 38, No. 157. (Jan., 1982), pp. 99-112, Jstor.  
  83. Padé approximation. (Chinese)
    Apresyan, L. A.
    Translated from the Russian by Xie Yong Cai. Yingyong Shuxue yu Jisuan Shuxue 1982, no. 4, 1--17, MathSciNet.  
  84. 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.  
  85. On Multivalued Exponential Approximations  
    Arieh Iserles  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 3. (Jun., 1981), pp. 480-499, Jstor.  
  86. 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.  
  87. Recursive Algorithms for Nonnormal Pade Tables  
    A. Bultheel  
    SIAM Journal on Applied Mathematics, Vol. 39, No. 1. (Aug., 1980), pp. 106-118, Jstor.  
  88. Recursive Algorithms for the Matrix Pade Problem  
    Adhemar Bultheel  
    Mathematics of Computation, Vol. 35, No. 151. (Jul., 1980), pp. 875-892, Jstor.  
  89. 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.  
  90. Padé approximation. (A survey). (Russian)
    Apresjan, L. A.
    Izv. Vyssh. Uchebn. Zaved. Radiofiz. 22 (1979), no. 6, 653--674, MathSciNet.  
  91. 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.  
  92. 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.  
  93. On the Newton-Padé approximation problem.
    Claessens, Guido
    J. Approximation Theory 22 (1978), no. 2, 150--160, MathSciNet.  
  94. Uniqueness of Pade Approximants From Series of Orthogonal Polynomials  
    Avram Sidi  
    Mathematics of Computation, Vol. 31, No. 139. (Jul., 1977), pp. 738-739, Jstor.  
  95. 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.  
  96. 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.  
  97. 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.  
  98. 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.  
  99. 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.  
  100. 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.  
  101. 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.  
  102. Pade Approximation to the Solution of the Ricatti Equation  
    Wyman Fair  
    Mathematics of Computation, Vol. 18, No. 88. (Oct., 1964), pp. 627-634, Jstor.  
  103. 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.  
  104. 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.  
  105. 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.  
  106. 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.  
  107. 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