Polynomial algebra for Birkhoff interpolants

[1]  Elías Berriochoa,et al.  Algorithms for solving Hermite interpolation problems using the Fast Fourier Transform , 2010, J. Comput. Appl. Math..

[2]  David R. Stoutemyer,et al.  Multivariate partial fraction expansion , 2009, ACCA.

[3]  Adhemar Bultheel,et al.  Algorithm 882: Near-Best Fixed Pole Rational Interpolation with Applications in Spectral Methods , 2008, TOMS.

[4]  Martin Berggren,et al.  Hybrid differentiation strategies for simulation and analysis of applications in C++ , 2008, TOMS.

[5]  N. Higham.  Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics) , 2008 .

[6]  Robert M Corless,et al.  Compact finite difference method for American option pricing , 2007 .

[7]  Charalampos Tsitouras,et al.  Runge–Kutta interpolants for high precision computations , 2007, Numerical Algorithms.

[8]  L. Hogben.  Handbook of Linear Algebra , 2006 .

[9]  Robert M. Corless,et al.  Compact finite difference method for integro-differential equations , 2006, Appl. Math. Comput..

[10]  Victor Y. Pan,et al.  Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations , 2005, Numerische Mathematik.

[11]  N. Higham.  The numerical stability of barycentric Lagrange interpolation , 2004 .

[12]  S. Hou,et al.  Inversion of confluent Vandermonde matrices , 2002 .

[13]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[14]  Luca Gemignani,et al.  Fast and stable computation of the barycentric representation of rational interpolants , 1996 .

[15]  Manuel Bronstein,et al.  Full partial fraction decomposition of rational functions , 1993, ISSAC '93.

[16]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[17]  Desmond J. Higham,et al.  Runge-Kutta Defect Control Using Hermite-Birkhoff Interpolation , 1991, SIAM J. Sci. Comput..

[18]  Claus Schneider,et al.  Hermite interpolation: The barycentric approach , 1991, Computing.

[19]  I. Gladwell,et al.  Shape-Preserving Local Interpolation for Plotting Solutions of ODEs , 1989 .

[20]  Henry C. Thacher,et al.  Applied and Computational Complex Analysis. , 1988 .

[21]  George G. Lorentz,et al.  Birkhoff Interpolation by G. G. Lorentz , 1984 .

[22]  B. D. Sivazlian,et al.  Partial fractions expansion , 1983 .

[23]  George G. Lorentz,et al.  Continuity of the Birkhoff Interpolation , 1982 .

[24]  G. Mühlbach,et al.  An algorithmic approach to Hermite-Birkhoff-interpolation , 1981 .

[25]  Francis Y. L. Chin,et al.  The Partial Fraction Expansion Problem and Its Inverse , 1977, SIAM J. Comput..

[26]  H. T. Kung,et al.  Fast Algorithms for Partial Fraction Decomposition , 1977, SIAM J. Comput..

[27]  T. J. Rivlin,et al.  Quadrature formulae and Hermite-Birkhoff interpolation , 1973 .

[28]  L. M. Milne-Thomson,et al.  The Calculus Of Finite Differences , 1934 .

[29]  H. W. Turnbull.  Note on Partial Fractions and Determinants , 1927 .

[30]  L. González-Vega,et al.  Barycentric Hermite Interpolants for Event Location in Initial-Value Problems , 2008 .

[31]  Brigitte Verdonk,et al.  Practical rational interpolation of exact and inexact data: theory and algorithms , 2008 .

[32]  Nicholas J. Higham,et al.  Functions of matrices - theory and computation , 2008 .

[33]  F. Uhlig,et al.  Numerical Behavior of the DQR Method for Rank-Structured Matrices , 2008 .

[34]  Karla Rost,et al.  Matrix exponentials and inversion of confluent Vandermonde matrices. , 2004 .

[35]  Lloyd N. Trefethen,et al.  Barycentric Lagrange Interpolation , 2004, SIAM Rev..

[36]  Robert M Corless,et al.  Bernstein Bases are Optimal , but , sometimes , Lagrange Bases are Better , 2004 .

[37]  L. Trefethen.  Spectral Methods in MATLAB , 2000 .

[38]  Joachim von zur Gathen,et al.  Modern Computer Algebra , 1998 .

[39]  Keith O. Geddes,et al.  Algorithms for computer algebra , 1992 .

[40]  Mei Han An,et al.  accuracy and stability of numerical algorithms , 1991 .

[41]  J. Fiala.  An algorithm for Hermite-Birkhoff interpolation , 1973 .

[42]  T. Broadbent.  Complex Variables , 1970, Nature.

[43]  John C. Butcher,et al.  A Multistep Generalization of Runge-Kutta Methods With Four or Five Stages , 1967, JACM.

[44]  George D. Birkhoff,et al.  General mean value and remainder theorems with applications to mechanical differentiation and quadrature , 1906 .