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1.

図書

図書
by L. Fox
出版情報: Oxford : Clarendon Press, 1964  xi, 328 p. ; 24 cm
シリーズ名: Monographs on numerical analysis
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2.

図書

図書
Philip E. Gill, Walter Murray, Margaret H. Wright
出版情報: Redwood City, Calif. : Addison-Wesley Pub. Co., Advanced Book Program, c1991  xvii, 426 p. ; 24 cm
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3.

図書

図書
Faddeeva, V. N. ; Benster, Curtis D.
出版情報: New York : Dover Publications, c1959  x, 252 p. ; 20 cm
シリーズ名: Dover books on mathematics
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4.

図書

図書
Lloyd N. Trefethen, David Bau, III
出版情報: Philadelphia : Society for Industrial and Applied Mathematics, c1997  xii, 361 p. ; 26 cm
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目次情報: 続きを見る
Preface
Fundamental: / Part I:
Matrix-vector multiplication / 1:
Orthogonal vectors and matrices / 2:
Norms / 3:
The singular value decomposition / 4:
More on the SVD / 5:
QR Factorization and Least Squares: / Part II:
Projectors / 6:
QR factorization / 7:
Gram-Schmidt orthogonalization / 8:
MATLAB / 9:
Householder triangularization / 10:
Least squares problems / 11:
Conditioning and Stability: / Part III:
Conditioning and condition numbers / 12:
Floating point arithmetic / 13:
Stability / 14:
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:
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