Introduction to numerical linear algebra / Christoph Börgers.

Format:

Book

Author/Creator:

Börgers, Christoph, author.

Contributor:

Society for Industrial and Applied Mathematics, publisher.

Series:

Other titles in applied mathematics.

[Other titles in applied mathematics] ; OT178

Language:

English

Subjects (All):

Algebras, Linear.

Numerical analysis.

Physical Description:

1 online resource (x, 348 pages) : illustrations.

Place of Publication:

Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), [2022]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

This textbook on numerical methods for linear algebra problems presents detailed explanations that beginning students can read on their own, allowing instructors to go beyond lecturing and making it suitable for a "flipped" classroom. The author covers several topics not commonly addressed in related introductory books, including diffusion, a toy model of computed tomography, global positioning systems, the use of eigenvalues in analyzing stability of equilibria, and multigrid methods. A detailed derivation and careful motivation of the QR method for eigenvalues starting from power iteration is also included, as is a discussion of the use of the SVD for grading.

Contents:

A few bits of linear algebra

Diffusion

Gaussian elimination

LU and PLU decompositions

Band matrices

Flop counts

Dot product and the Euclidean norm

The p-norms

Matrix norms

The condition number

The ill-conditioning of discrete equilibrium diffusion problem

The ill-conditioning of some (not all) interpolation problems

Ill-conditioned problems vs. unstable numerical algorithms

Nonsquare linear systems

Orthogonal matrices and symmetric matrices

QR decomposition

Positive definite matrices and Cholesky decomposition

A reason to care about eigenvalues : stability of equilibria

Some basic facts about eigenvalues and eigenvectors

Power iteration

Block power iteration for symmetric matrices

QR iteration

Singular value decomposition (SVD)

Some of the many applications of the SVD

Jacobi and Gauss-Seidel iteration

Theory of linear iterative methods

The multigrid method

Appendix A. Taylor expansions

Appendix B. Solutions to some of the exercises.

Notes:

Description based on title page of print version.

Includes bibliographical references (pages 345-346) and index.

ISBN:

1-61197-692-8

Publisher Number:

OT178 SIAM