Numerical linear algebra : theory and applications

✍ Scribed by Beilina, Larisa; Karchevskii, Evgenii; Karchevskii, Mikhail

• Publisher: Springer
• Year: 2017
• Tongue: English
• Leaves: 457
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xii
Preliminaries (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 1-54
Vector Spaces (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 55-68
Inner Product Spaces (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 69-92
Linear Operators (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 93-162
Canonical Forms and Factorizations (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 163-208
Vector and Matrix Norms (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 209-229
Elements of Perturbation Theory (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 231-248
Solving Systems of Linear Equations (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 249-289
Numerical Solution of Linear Least Squares Problems (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 291-343
Algorithms for the Nonsymmetric Eigenvalue Problem (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 345-374
Algorithms for Solution of Symmetric Eigenvalue Problems (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 375-405
Introduction to Iterative Methods for the Solution of Linear Systems (Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii)....Pages 407-439
Back Matter ....Pages 441-450

✦ Subjects

Algebras, Linear