Numerical linear algebra

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Numerical linear algebra / Lloyd N. Trefethen, David Bau, III

資料種別:

図書

出版情報:

Philadelphia : Society for Industrial and Applied Mathematics, c1997

形態:

xii, 361 p. ; 26 cm

著者名:

ISBN:

9780898713619 [0898713617]

書誌ID:

BA30815324

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references (p. 343-352) and index

主題:

Algebras, Linear; Numerical calculations

言語:

英語

目次情報:

Preface

Fundamental: / Part I：

Matrix-vector multiplication / 1：

Orthogonal vectors and matrices / 2：

Norms / 3：

The singular value decomposition / 4：

More on stability / 15：

Stability of householder triangularization / 16：

Stability of back substitution / 17：

Conditioning of least squares problems / 18：

Stability of least squares algorithms / 19：

Systems of Equations: / Part IV：

Gaussian elimination / 20：

Pivoting / 21：

Stability of Gaussian elimination / 22：

Cholesky factorization / 23：

Eigenvalues: / Part V：

Eigenvalue problems / 24：

Overview of Eigenvalue algorithms / 25：

Reduction to Hessenberg or tridiagonal form / 26：

Rayleigh quotient, inverse iteration / 27：

QR algorithm without shifts / 28：

QR algorithm with shifts / 29：

Other Eigenvalue algorithms / 30：

Computing the SVD / 31：

Iterative Methods: / Part VI：

Overview of iterative methods / 32：

The Arnoldi iteration / 33：

How Arnoldi locates Eigenvalues / 34：

GMRES / 35：

The Lanczos iteration / 36：

From Lanczos to Gauss quadrature / 37：

Conjugate gradients / 38：

Biorthogonalization methods / 39：

Preconditioning / 40：

Appendix

Notes

Bibliography

Index

Preface

Fundamental: / Part I：

Matrix-vector multiplication / 1：

Orthogonal vectors and matrices / 2：

Norms / 3：

The singular value decomposition / 4：

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