Biorthogonality and its Applications to Numerical Analysis  book cover
1st Edition

Biorthogonality and its Applications to Numerical Analysis

ISBN 9780824786168
Published November 27, 1991 by CRC Press
184 Pages

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Book Description

This book explores the use of the concept of biorthogonality and discusses the various recurrence relations for the generalizations of the method of moments, the method of Lanczos, and the biconjugate gradient method. It is helpful for researchers in numerical analysis and approximation theory.

Table of Contents

Introduction Preliminaries Biorthogonality and Applications Orthogonality for Polynomials Interpolation and Projection Kernel The Interpolation Operator The Method of Moments Lanczos' Method The Bi-conjugate Gradient Method Fredholm Equation and Padé-Type Approximants Adjacent Biorthogonal Families One-Step Forumlas Multistep Formulas Applications Sequence Transformations Linear Multistep Methods Approximation of Series Biorthogonal Polynomials Statistics and Least Squares Appendix 1: A Direct Proof of the Christoffel-Darboux Identity and a Consequence Appendix 2: Duality in Padé-Type Approximation Appendix 3: Sylvester's and Schweins' Identities in a Vector Space References

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