Numerical Linear Algebra and Matrix Factorizations

Numerical Linear Algebra and Matrix Factorizations

Author: Tom Lyche

Publisher: Springer

ISBN: 3030364674

Category: Mathematics

Page: 371

View: 290

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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.
Numerical Linear Algebra and Matrix Factorizations
Language: en
Pages: 371
Authors: Tom Lyche
Categories: Mathematics
Type: BOOK - Published: 2020-04-13 - Publisher: Springer

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
Exercises in Numerical Linear Algebra and Matrix Factorizations
Language: en
Pages: 265
Authors: Tom Lyche, Georg Muntingh, √ėyvind Ryan
Categories: Mathematics
Type: BOOK - Published: 2020-11-02 - Publisher: Springer Nature

To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory
Numerical Linear Algebra and Matrix Factorizations
Language: en
Pages: 371
Authors: Tom Lyche
Categories: Mathematics
Type: BOOK - Published: 2020-03-02 - Publisher: Springer Nature

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
Numerical Linear Algebra for Applications in Statistics
Language: en
Pages: 221
Authors: James E. Gentle
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of
Numerical Linear Algebra
Language: en
Pages: 361
Authors: Lloyd N. Trefethen, David Bau, III
Categories: Mathematics
Type: BOOK - Published: 1997-06-01 - Publisher: SIAM

Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra.