Details

Subject(s)

• Algebras, Linear [Browse]
• Numerical analysis [Browse]

Publisher

• Society for Industrial and Applied Mathematics [Browse]

Series

• Other titles in applied mathematics. [More in this series]
• [Other titles in applied mathematics] ; OT178

Restrictions note

Restricted to subscribers or individual electronic text purchasers.

Summary note

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.

Bibliographic references

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

System details

• Mode of access: World Wide Web.
• System requirements: Adobe Acrobat Reader.

Source of description

Description based on title page of print version.

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.

Show 26 more Contents items

Other format(s)

Also available in print version.

ISBN

1-61197-692-8

Publisher no.

OT178

LCCN

2021044784

Doi

• 10.1137/1.9781611976922

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