Analysis of methods for matrix computations: Basic methods

Abstract

This monograph is an introduction to the basic methods used in matrix computations. It grows up from the linear algebra basics (chapter 1), and touches functional analysis, especially analysis of operators on finite dimensional spaces.

Individual chapters are devoted to the Schur's theorem (chap. 2), orthogonal matrices and QR decomposition (chap. 3), Gauss elimination and LU decomposition (chap. 4), singular value decomposition (chap. 5), least squares problems (chap. 6), approximation of eigenvalues using Lanczos and Arnoldi algorithms (chap. 7), metod of conjugate gradients (chap. 8), and Krylov subspaces methods in general (chap. 9).

Keywords

• linear algebra
• matrix computations
• Schur theorem
• QR decomposition
• LU decomposition
• Cholesky decomposition
• singular value decomposition
• least squares problem
• Arnoldi method
• Lanczos method
• conjugate gradient method
• Krylov subspace methods