Numerical linear algebra : an introduction
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Bibliographic Information
Numerical linear algebra : an introduction
（Cambridge texts in applied mathematics）
Cambridge University Press, 2018
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Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of Contents
- 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.
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