Numerical Linear Algebra: Theory and Applications / by Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii.

Format:

Book

Author/Creator:

Beilina, Larisa., Author.

Karchevskii, Evgenii., Author.

Karchevskii, Mikhail., Author.

Language:

English

Subjects (All):

Matrix theory.

Algebra.

Linear and Multilinear Algebras, Matrix Theory.

Local Subjects:

Linear and Multilinear Algebras, Matrix Theory.

Physical Description:

1 online resource (XIV, 450 p. 15 illus., 14 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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 eigen problems.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.

Contents:

Preface

1. Preliminaries

2. Vector Spaces

3. Inner Product Spaces

4. Linear Operators

5. Canonical Forms and Factorizations

6. Vector and Matrix Norms

7. Elements of the Perturbation Theory

8. Solving Systems of Linear Equations

9. Numerical solution of Linear Least Squares Problems

10. Algorithms for the Nonsymmetric Eigenvalue Problem

11. Algorithms for Solution of Symmetric Eigenvalue problem

12. Introduction to Iterative Methods for Solution of Linear Systems

A. Matlab Programs

References.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-57304-7

OCLC:

1066180442