Book Details
Matrices, Moments and Quadrature with Applications
Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization.
This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
Part 1. Theory
Chapter 1. Introduction
Chapter 2. Orthogonal Polynomials
Chapter 3. Properties of Tridiagonal Matrices
Chapter 4. The Lanczos and Conjugate Gradient Algorithms
Chapter 5. Computation of the Jacobi Matrices
Chapter 6. Gauss Quadrature
Chapter 7. Bounds for Bilinear Forms
Chapter 8. Extensions to Nonsymmetric Matrices
Chapter 9. Solving Secular Equations
Applications
Chapter 10. Examples of Gauss Quadrature Rules
Chapter 11. Bounds and Estimates for Elements of Functions of Matrices
Chapter 12. Estimates of Norma of Errors in the Conjugate Gradient Algorithm
Chapter 13. Least Squares Problems
Chapter 14. Total Least Squares
Chapter 15. Discrete III-Posed Problems
Bibliography
Index
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