# Numerical Linear Algebra: An Introduction (Cambridge Texts in Applied Mathematics)

Cambridge University Press, 11/16/2017

EAN 9781107147133, ISBN10: 1107147131

Hardcover, 418 pages, 23.5 x 15.7 x 2.8 cm

Language: English

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

Part I. Preliminaries

1. Introduction

2. Error, stability and conditioning

Part II. Basic Methods

3. Direct methods for solving linear systems

4. Iterative methods for solving linear systems

5. Calculation of eigenvalues

Part III. Advanced Methods

6. Methods for large sparse systems

7. Methods for large dense systems

8. Preconditioning

9. Compressed sensing

References

Index.