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1.

図書

図書
Per-Olov Löwdin and Quantum Theory Project, University of Florida
出版情報: New York : John Wiley & Sons, c1998  xi, 458 p. ; 25 cm
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2.

図書

図書
Michael W. Frazier
出版情報: New York ; Tokyo : Springer, c1999  xvi, 501 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
Background: Complex Numbers and Linear Algebra / 1:
Real Numbers and Complex Numbers / 1.1:
Complex Series, Euler's Formula, and the Roots of Unity / 1.2:
Vector Spaces and Bases / 1.3:
Linear Transformations, Matrices, and Change of Basis / 1.4:
Diagonalization of Linear Transformations and Matrices / 1.5:
Inner Products, Orthonormal Bases, and Unitary Matrices / 1.6:
The Discrete Fourier Transform / 2:
Basic Properties of the Discrete Fourier Transform / 2.1:
Translation-Invariant Linear Transformations / 2.2:
The Fast Fourier Transform / 2.3:
Wavelets on $bZ_N$ / 3:
Construction of Wavelets on $bZ_N$: The First Stage / 3.1:
Construction of Wavelets on $bZ_N$: The Iteration Step / 3.2:
Examples and Applications / 3.3:
Wavelets on $bZ$ / 4:
$ ell ^2(bZ)$ / 4.1:
Complete Orthonormal Sets in Hilbert Spaces / 4.2:
$L^2([- pi , pi ))$ and Fourier Series / 4.3:
The Fourier Transform and Convolution on $ ell ^2(bZ)$ / 4.4:
First-Stage Wavelets on $bZ$ / 4.5:
The Iteration Step for Wavelets on $bZ$ / 4.6:
Implementation and Examples / 4.7:
Wavelets on $bR$ / 5:
$L^2(bR)$ and Approximate Identities / 5.1:
The Fourier Transform on $bR$ / 5.2:
Multiresolution Analysis and Wavelets / 5.3:
Construction of Multiresolution Analyses / 5.4:
Wavelets with Compact Support and Their Computation / 5.5:
Wavelets and Differential Equations / 6:
The Condition Number of a Matrix / 6.1:
Finite Difference Methods for Differential Equations / 6.2:
Wavelet-Galerkin Methods for Differential Equations / 6.3:
Bibliography
Index
Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
3.

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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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:
5.

図書

図書
Steven Roman
出版情報: New York ; Tokyo : Springer-Verlag, c1992  xii, 363 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 135
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6.

図書

図書
Larry Smith
出版情報: New York : Springer, c1998  xii, 452 p. ; 24 cm
シリーズ名: Undergraduate texts in mathematics
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7.

図書

図書
Rami Shakarchi
出版情報: New York ; Tokyo : Springer-Verlag, c1996  xi, 183 p. ; 24 cm
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目次情報: 続きを見る
Vector Spaces
Matrices
Linear Mappings
Linear Maps and Matrices
Scalar Products and Orthogonality
Determinants
Symmetric, Hermitian, and Unitary Operators
Eigenvectors and Eigenvalues
Polynomials and Matrices
Triangulation of Matrices and Linear Maps
Polynomials and Primary Decomposition
Convex Sets
Vector Spaces
Matrices
Linear Mappings
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