# Numerical Linear Algebra and Matrix Factorizations

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

### 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 linear algebra numerical stability QR decomposition singular value decomposition tensor products iterative measures

#### Authors and affiliations

1. 1.Blindern, University of OsloOsloNorway

The author has a long experience at the university level, teaching numerical analysis, numerical linear algebra and matrix theory, mathematical optimization, approximation theory, and computer aided geometric design.

He has received the Dagstuhl foundation’s John Gregory Memorial Award for "Outstanding contributions to geometric modeling" and is a member of Norwegian Academy of Science and Letters.

He has published more than 90 papers in leading international journals and refereed proceedings, edited 17 books and is on the editorial board of 4 international journals. Jointly with Prof. Jean-Louis Merrien,  he has published the book “Exercises in Computational Mathematics with MATLAB “ published by Springer in 2014.

### Bibliographic information

• Book Title Numerical Linear Algebra and Matrix Factorizations
• Authors Tom Lyche
• Series Title Texts in Computational Science and Engineering
• Series Abbreviated Title Texts in Computat. Science
• 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 Mathematics and Statistics (R0)
• Hardcover ISBN 978-3-030-36467-0
• Softcover ISBN 978-3-030-36470-0
• eBook ISBN 978-3-030-36468-7
• Series ISSN 1611-0994
• Series E-ISSN 2197-179X
• Edition Number 1
• Number of Pages XXIII, 371
• Number of Illustrations 144 b/w illustrations, 37 illustrations in colour
• Topics
• Buy this book on publisher's site

## Reviews

“It is more suitable for students with a few more advanced courses that include at least some real analysis and introductory numerical analysis.” (Tom Lyche, MAA Reviews, November 7, 2020)