New York: Springer, 2017. — 457 p. — ISBN: 3319573020.
This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numerical algorithms illustrated by computer programs written in MatLAB are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.
Preliminaries
Vector Spaces
Inner Product Spaces
Linear Operators
Canonical Forms and Factorizations
Vector and Matrix Norms
Elements of Perturbation Theory
Solving Systems of Linear Equations
Numerical Solution of Linear Least Squares Problems
Algorithms for the Nonsymmetric Eigenvalue Problem
Algorithms for Solution of Symmetric Eigenvalue Problems
Introduction to Iterative Methods for the Solution of Linear Systems