Preface

Problems of numerical linear algebra arise in all fields of modern science. Important examples are computational fluid dynamics, solid mechanics, electrical networks, signal analysis, and optimization. In our book we present an extended basic theory of linear algebra including such topics as matrix algebra, theory of linear systems of equations, spectral theory, vector and matrix norms, combined with the most important direct and iterative numerical methods for solution of linear systems of equations, least squares problems, and eigenproblems. In this book we wanted to combine a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Most of the presented numerical algorithms are illustrated by computer programs written in MATLAB, which are given in the electronic supplementary material that can be found on SpringerLink. These programs allow the reader to obtain experience in implementation and evaluation of numerical algorithms for the problems described in the book and give possibility to apply them to the solution of the computer exercises presented in this book. They can also give the reader a better understanding of professional numerical software for the solution of real-life problems in numerical linear algebra. This book is suitable for use as course material in a oneor two-semester course on numerical linear algebra, matrix computations, or large sparse matrices at the advanced undergraduate or graduate level. We recommend using the material of Chapters 1–7 for courses in the theoretical aspects of linear algebra, or as the first part for a course in numerical linear algebra. In addition to traditional content for courses in linear algebra for students specializing in the physical and mathematical sciences, we include in these chapters some sections that can be useful as course material for special courses on various applications of linear algebra. We hope that this material will also be of interest to scientists. We recommend Chapters 8–12 for courses related to numerical linear algebra, or as the second part of a course in numerical linear algebra. The material of Chapters 8–12 follows the book of Demmel [23]. Compared with [23], we present the numerical material of Chapters 8–12 in amore concise form, which is appropriate to a one-semester course in numerical linear algebra at the undergraduate level. We also enrich our Chapters 8–12 with numerical examples,