Numerical Linear Algebra: Theory and Applications

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.

• 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.

“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)