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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.
List of 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.
About the author
Larisa Beilina is an Associate Professor in the Department of Mathematical Sciences at Chalmers University of Technology and Gothenburg University.
Evgenii Karchevskii and Mikhail Karchevskii are both professors at the Institute of Computer Mathematics and Information Technologies at Kazan Federal University, Russia.
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 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.
Additional text
“It provides a rock-solid theoretical background in a very approachable manner, a good overview of classical algorithms of numerical linear algebra and a good framework and guidance for numerical experiments.” (Cyril Fischer, zbMATH 1396.65001, 2018)
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"It provides a rock-solid theoretical background in a very approachable manner, a good overview of classical algorithms of numerical linear algebra and a good framework and guidance for numerical experiments." (Cyril Fischer, zbMATH 1396.65001, 2018)
