Numerical Linear Algebra

Name: Numerical Linear Algebra
Price: 32.52 USD
Availability: InStock
ISBN: 9780898713619

ISBN-10: 0898713617

ISBN-13: 9780898713619

Edition: 1997

Authors: Lloyd N. Trefethen, David Bau III

List price: $74.50

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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…

Book details

List price: $74.50
Copyright year: 1997
Publisher: Society for Industrial and Applied Mathematics
Publication date: 6/30/1997
Binding: Paperback
Pages: 373
Size: 7.25" wide x 10.25" long x 0.75" tall
Weight: 1.716
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