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Numerical Linear Algebra

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ISBN-10: 0898713617

ISBN-13: 9780898713619

Edition: 1997

Authors: Lloyd N. Trefethen, David Bau

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Description:

This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and…    
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Book details

Copyright year: 1997
Publisher: Society for Industrial and Applied Mathematics
Binding: Paperback
Pages: 373
Size: 7.25" wide x 10.25" long x 0.75" tall
Weight: 1.606
Language: English

Preface
Fundamental:
Matrix-vector multiplication
Orthogonal vectors and matrices
Norms
The singular value decomposition
More on the SVD
QR Factorization and Least Squares:
Projectors
QR factorization
Gram-Schmidt orthogonalization
MATLAB
Householder triangularization
Least squares problems
Conditioning and Stability:
Conditioning and condition numbers
Floating point arithmetic
Stability
More on stability
Stability of householder triangularization
Stability of back substitution
Conditioning of least squares problems
Stability of least squares algorithms
Systems of Equations:
Gaussian elimination
Pivoting
Stability of Gaussian elimination
Cholesky factorization
Eigenvalues:
Eigenvalue problems
Overview of Eigenvalue algorithms
Reduction to Hessenberg or tridiagonal form
Rayleigh quotient, inverse iteration
QR algorithm without shifts
QR algorithm with shifts
Other Eigenvalue algorithms
Computing the SVD
Iterative Methods:
Overview of iterative methods
The Arnoldi iteration
How Arnoldi locates Eigenvalues
GMRES
The Lanczos iteration
From Lanczos to Gauss quadrature
Conjugate gradients
Biorthogonalization methods
Preconditioning
Appendix
Notes
Bibliography
Index