# Numerical Linear Algebra and Matrix Factorizations

• Tom Lyche
Textbook

Part of the Texts in Computational Science and Engineering book series (TCSE, volume 22)

1. Front Matter
Pages i-xxiii
2. Tom Lyche
Pages 1-24
3. ### LU and QR Factorizations

1. Front Matter
Pages 25-25
2. Tom Lyche
Pages 27-55
3. Tom Lyche
Pages 57-81
4. Tom Lyche
Pages 83-98
5. Tom Lyche
Pages 99-126
4. ### Eigenpairs and Singular Values

1. Front Matter
Pages 127-127
2. Tom Lyche
Pages 129-151
3. Tom Lyche
Pages 153-168
5. ### Matrix Norms and Least Squares

1. Front Matter
Pages 169-169
2. Tom Lyche
Pages 171-198
3. Tom Lyche
Pages 199-222
6. ### Kronecker Products and Fourier Transforms

1. Front Matter
Pages 223-223
2. Tom Lyche
Pages 225-236
3. Tom Lyche
Pages 237-250
7. ### Iterative Methods for Large Linear Systems

1. Front Matter
Pages 251-251
2. Tom Lyche
Pages 253-277
3. Tom Lyche
Pages 279-313
8. ### Eigenvalues and Eigenvectors

1. Front Matter
Pages 315-315
2. Tom Lyche
Pages 317-334
3. Tom Lyche
Pages 335-347
9. ### Appendix

1. Front Matter
Pages 349-349
2. Tom Lyche
Pages 351-353
10. Back Matter
Pages 355-371

### Introduction

After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them.

Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones.

The main characteristics of this book are as follows:

It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study.

The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.

### Keywords

numerical linear algebra matrix theory MATLAB programming linear systems least squares eigenvalue problems nonlinear equations scientific computing

#### Authors and affiliations

• Tom Lyche
• 1
1. 1.Blindern, University of OsloOsloNorway

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-030-36468-7
• Copyright Information Springer Nature Switzerland AG 2020
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics
• Print ISBN 978-3-030-36467-0
• Online ISBN 978-3-030-36468-7
• Series Print ISSN 1611-0994
• Series Online ISSN 2197-179X
• Buy this book on publisher's site