Overview
- Detailed proofs of practically all results making it suitable for self-study
- Detailed algorithms in Matlab
- The book is self-contained, assuming only first year calculus
Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 22)
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Table of contents (16 chapters)
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Front Matter
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Eigenpairs and Singular Values
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Front Matter
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Matrix Norms and Least Squares
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Front Matter
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Kronecker Products and Fourier Transforms
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Front Matter
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Iterative Methods for Large Linear Systems
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Front Matter
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Eigenvalues and Eigenvectors
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Front Matter
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Keywords
About this book
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.
Reviews
Authors and Affiliations
About the author
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
DOI: https://doi.org/10.1007/978-3-030-36468-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-36467-0Published: 03 March 2020
Softcover ISBN: 978-3-030-36470-0Published: 03 March 2021
eBook ISBN: 978-3-030-36468-7Published: 02 March 2020
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: Linear and Multilinear Algebras, Matrix Theory, Algorithms, Computational Science and Engineering, Numerical Analysis