Numerical Linear Algebra: Theory and Applications

1. Front Matter

   Pages i-xiv

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2. Preliminaries

   • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

   Pages 1-54

3. Vector Spaces

   • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

   Pages 55-68

4. Inner Product Spaces

   • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

   Pages 69-92

5. Linear Operators

   • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

   Pages 93-162

6. Canonical Forms and Factorizations

   • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

   Pages 163-208

7. Vector and Matrix Norms

   • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

   Pages 209-229

8. Elements of Perturbation Theory

   • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

   Pages 231-248

9. Solving Systems of Linear Equations

   • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

   Pages 249-289

10. Numerical Solution of Linear Least Squares Problems

    • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

    Pages 291-343

11. Algorithms for the Nonsymmetric Eigenvalue Problem

    • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

    Pages 345-374

12. Algorithms for Solution of Symmetric Eigenvalue Problems

    • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

    Pages 375-405

13. Introduction to Iterative Methods for the Solution of Linear Systems

    • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

    Pages 407-439

14. Erratum to: Numerical Linear Algebra: Theory and Applications

    • Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii

    Pages E1-E1

15. Back Matter

    Pages 441-450

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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.

• Eigenvalues
• Eigenvectors
• Large Sparse Matrices
• Matrix Algorithms
• Matrix Computatioms
• Numerical Linear Algebra
• matrix theory

 “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)  

• Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden

  Larisa Beilina

• Department of Applied Mathematics, Kazan Federal University, Kazan, Tatarstan Republic, Russia

  Evgenii Karchevskii

• Department of Computational Mathematics, Kazan Federal University, Kazan, Tatarstan Republic, Russia

  Mikhail Karchevskii

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. 

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