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Original Articles

Padé error estimates for the logarithm of a matrix

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Pages 707-730 | Received 11 Oct 1988, Published online: 17 Apr 2007

REFERENCES

  • Baker , G. , 1975 , Essentials of Pade Approximates , ( New York : Academic Press ).
  • Baker , G. , and Graves-Morris , P. , Pade Approximants , Encyclopedia of Mathematics and its Applications , Vols 13 and 14 , ( 1981 , London : Addison-Wesley ). edited by Gian-Carlo Rota
  • Brezinski , C. , Pade approximants and orthogonal polynomials. Pade and Rational Approximation Theory and Applications , edited by E. Saff , and R. Varga , ( 1977 , New York : Academic Press ), pp. 3 – 14 .
  • CauChy , M. , 1821 , Cours d'Analyse tie L'Écote Royale Poly technique: l.re Partie. Analyse Algébrique , L'imprimerie Royal , Paris .
  • Euler , L. , 1748 , Introductio in Analysin Infinitorum , Lausanne , Vol. 1 .
  • Frobenius , G. , 1881 , Über Relationen Zwischen den Näherüngsbriichen von Potenzreihen. Journal für die reine und angewandte Mathematik , ( Crelle ), 90 , 1 – 17 .
  • Gauss , C. , 1812 , Disquisitiones generates circa seriem infinitam. Thesis, Göttingen , published in Gesammelte Werke Gottingen , 1866 .
  • Golub , G. , and Van Loan , C , 1983 , Matrix Computations , ( Baltimore : Johns Hopkins University Press ).
  • Gradshteyn , I. , and Ryzhik , I. , 1965 , Table of Integrals, Series, and Products , ( New York : Academic Press ).
  • Jacobi , C. , 1846 , Über die Darstellung einer Reihe Gegebner Werthe durch eine Gebrochne Rationale Function. Journal für die reine und angewandte Mathematik , ( Crelle ), 30 , 127 – 156 .
  • Kenney , C. , and Laub , A. J. , 1989 , Condition estimates for matrix functions , SIAM Journal of Matrix Analysis and Applications , 10 , 191 – 209 .
  • Kummer , E. , 1836 , Über die Hypergeometrische Reihe F(α,β, x) . Journal für die reine und angewandte Mathematik , 15 .
  • Lancaster , P. , and Tismenetsky , M. , 1985 , The Theory of Matrices , second edition ( New York : Academic Press ).
  • Lastman , G. , Puthenpura , S. , and Sinha , N , 1984 , Algorithm for the identification of continuous-time multivariable systems from their discrete-time models. Electronics Letters , 20 , 918 – 919 .
  • Luke , Y. , 1969 , The Special Functions and Their Approximations , ( New York : Academic Press ).
  • Padé , H. , 1892 , Sur la representation approchée d'une fonction pour des fractions rationelles. Annates Scientifiques de I'École Normale Supérieure (Supplement) , 9 , 1 – 93 .
  • Puthenpura , S. , and Sinha , N. , 1984 , Transformation of continuous-time model of a linear multivariable system from its discrete-time model. Electronics Letters , 20 , 737 – 738 .
  • Rigmann , G. , 1857 , P-Funktionen. Gesammelte Mathematische Werke , Göttingen , republished Leipzig > , 1892 .
  • Sinha , N. , and Lastman , G. , 1981 , Transformation algorithm for identification of continuous-time multivariable systems from discrete data. Electronics Letters , 17 , 779 – 780 .
  • Slater , L. , 1966 , Generalized Hypergeometric Functions , ( Cambridge , U .K.: Cambridge University Press ).
  • Szegö , G. , 1939 , Orthogonal Polynomials , ( Providence , RI : American Mathematical Society ).
  • Wallis , J. , 1655 , Arithmetica Infinitorium. Opera Malhemalica , Vol. I , pp. 355 – 478 . Oxoniae e Theatro Shedoniano (y1695). Reprinted by Georg Olms Verlag, Hildeshein, New York( 1972) .

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