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1.

図書

図書
Yousef Saad
出版情報: Philadelphia : Society for Industrial and Applied Mathematics(SIAM), c2011  xvi, 276 p. ; 23 cm
シリーズ名: Classics in applied mathematics ; 66
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目次情報: 続きを見る
Preface to the Classics Edition
Preface
Background in matrix theory and linear algebra / 1:
Sparse matrices / 2:
Perturbation theory and error analysis / 3:
The tools of spectral approximation / 4:
Subspace iteration / 5:
Krylov subspace methods / 6:
Filtering and restarting techniques / 7:
Preconditioning techniques / 8:
Non-standard eigenvalue problems / 9:
Origins of matrix eigenvalue problems / 10:
References
Index
Preface to the Classics Edition
Preface
Background in matrix theory and linear algebra / 1:
2.

図書

図書
Michihiro Kitahara
出版情報: Amsterdam ; Tokyo : Elsevier, 1985  viii, 281 p. ; 25 cm
シリーズ名: Studies in applied mechanics ; 10
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3.

図書

図書
Alexander Weinstein and William Stenger
出版情報: New York : Academic Press, 1972  xi, 236 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 89
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目次情報: 続きを見る
Preface
Overview / 1:
Methods of Operator Approximation in System Modelling / I:
Nonlinear Operator Approximation with Preassigned Accuracy / 2:
Introduction / 2.1:
Generic formulation of the problem / 2.2:
Operator approximation in space C([0; 1]) / 2.3:
Operator approximation in Banach spaces by polynomial operators / 2.4:
Approximation on compact sets in topological vector spaces / 2.5:
Approximation on noncompact sets in Hilbert spaces / 2.6:
Special results for maps into Banach spaces / 2.7:
Concluding remarks / 2.8:
Interpolation of Nonlinear Operators 65 / 3:
Lagrange interpolation in Banach spaces / 3.1:
Weak interpolation of nonlinear operators / 3.3:
Some related results / 3.4:
Realistic Operators and their Approximation / 3.5:
Formalization of concepts related to description of real-world objects / 4.1:
Approximation of RÂícontinuous operators / 4.3:
Methods of Best Approximation for Nonlinear Operators / 4.4:
Best Approximation of nonlinear operators in Banach spaces: Deterministic case / 5.1:
Estimation of mean and covariance matrix for random vectors / 5.3:
Best Hadamard-quadratic approximation / 5.4:
Best polynomial approximation / 5.5:
Best causal approximation / 5.6:
Best hybrid approximations / 5.7:
Optimal Estimation of Random Vectors / 5.8:
Computational Methods for Optimal Filtering of Stochastic Signals / 6:
Optimal linear Filtering in Finite dimensional vector spaces / 6.1:
Optimal linear Filtering in Hilbert spaces / 6.3:
Optimal causal linear Filtering with piecewise constant memory / 6.4:
Optimal causal polynomial Filtering with arbitrarily variable memory / 6.5:
Optimal nonlinear Filtering with no memory constraint / 6.6:
Computational Methods for Optimal Compression and Reconstruction of Random Data / 6.7:
Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) / 7.1:
Rank-constrained matrix approximations / 7.3:
Generic PCA{KLT / 7.4:
Optimal hybrid transform based on Hadamard-quadratic approximation / 7.5:
Optimal transform formed by a combination of nonlinear operators / 7.6:
Optimal generalized hybrid transform / 7.7:
Bibliography / 7.8:
Index
Preface
Overview / 1:
Methods of Operator Approximation in System Modelling / I:
4.

図書

図書
Beresford N. Parlett
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1980  xix, 348 p. ; 24 cm
シリーズ名: Prentice-Hall series in computational mathematics
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5.

図書

図書
Charles R. Johnson, Carlos M. Saiago
出版情報: Cambridge : Cambridge University Press, 2018  xxii, 291 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 211
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6.

図書

図書
F.V. Atkinson
出版情報: New York : Academic Press, c1972  xi, 209 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 82-1 . Multiparameter eigenvalue problems / [by] F.V. Atkinson ; v. 1
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7.

図書

図書
Isaac Chavel ; with a chapter by Burton Randol ; with appendix by Jozef Dodziuk
出版情報: Orlando ; Tokyo : Academic Press, 1984  xiv, 362 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 115
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目次情報: 続きを見る
Preface
The Laplacian
The Basic Examples
Curvature
Isoperimetric Inequalities
Eigenvalues and Kinematic Measure
The Heat Kernel for Compact Manifolds
The Dirichlet Heat Kernel for Regular Domains
The Heat Kernel for Noncompact Manifolds
Topological Perturbations with Negligible Effect
Surfaces of Constant Negative Curvature
The Selberg Trace Formula
Miscellanea
Laplacian on Forms
Bibliography
Index
Preface
The Laplacian
The Basic Examples
8.

図書

図書
Oktay Veliev
出版情報: Cham : Springer, c2019  xii, 326 p. ; 25 cm
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