Biorthogonality and its Applications to Numerical Analysis

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 Pade-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 Pade-Type Approximation Appendix 3: Sylvester's and Schweins' Identities in a Vector Space References