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求解代數特徵值問題模板實用指南：國際著名數學圖書（簡體書）
商品資訊
ISBN13：9787302244967
替代書名：Templates of the Solution of Algebraic Eigenvalue Problems：A Practical Guide
出版社：清華大學出版社(大陸)
作者：ZHAOJUNBAI.JAMESDEMMEL
出版日：2011/02/01
裝訂：平裝
商品簡介
作者簡介
目次
商品簡介
《求解代數特征值問題模板實用指南(影印版)》內容簡介：large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. this book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. it organizes this large body of material to make it accessible for the first time to experts as well as many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.
the algorithms and software at the leaves of the decision tree range from the classical qr algorithm, which is most suitable for small dense matrices, to iterative algorithms for very large generalized eigenvalue problems. algorithms are presented in a unified style as templates,with different levels of detail suitable for readers ranging from beginning students to experts. the authors comprehensive treatment includes a treasure of further bibliographic information.
the algorithms and software at the leaves of the decision tree range from the classical qr algorithm, which is most suitable for small dense matrices, to iterative algorithms for very large generalized eigenvalue problems. algorithms are presented in a unified style as templates,with different levels of detail suitable for readers ranging from beginning students to experts. the authors comprehensive treatment includes a treasure of further bibliographic information.
作者簡介
作者：（美國）白照音（Xhaojun Bai） （美國）James Demmel （美國）Jack Dongarra 等
目次
list of symbols and acronyms
list of iterative algorithm templates
list of direct algorithms
list of figures
list of tables
1 introduction
1.1 why eigenvalue templates?
1.2 intended readership
1.3 using the decision tree to choose a template
1.4 what is a template?
1.5 organization of the book
2 a brief tour of eigenproblems
2.1 introduction
2.1.1 numerical stability and conditioning
2.2 hermitian eigenproblems
j. demmel
2.2.1 eigenvalues and eigenvectors
2.2.2 invariant subspaces
2.2.3 equivalences (similarities)
2.2.4 eigendecompositions
2.2.5 conditioning
2.2.6 specifying an eigenproblem
2.2.7 related eigenproblems
2.2.8 example
2.3 generalized hermitian eigenproblems
j. dernrnel
2.3.1 eigenvalues and eigenvectors
2.3.2 eigenspaces
2.3.3 equivalences (congruences)
2.3.4 eigendecompositions
2.3.5 conditioning
2.3.6 specifying an eigenproblem
2.3.7 related eigenproblems
2.3.8 example
2.4 singular value decomposition
j. demrnel
2.4.1 singular values and singular vectors
2.4.2 singular subspaces
2.4.3 equivalences
2.4.4 decompositions
2.4.5 conditioning
2.4.6 specifying a singular value problem
2.4.7 related singular value problems
2.4.8 example
2.5 non-hermitian eigenproblerns
j. demmel
2.5.1 eigenvalues and eigenvectors
2.5.2 invariant subspaces
2.5.3 equivalences (similarities)
2.5.4 eigendecompositions
2.5.5 conditioning
2.5.6 specifying an eigenproblem
2.5.7 related eigenproblems
2.5.8 example
2.6 generalized non-hermitian eigenproblerns
j. demmel
2.6.1 eigenvalues and eigenvectors
2.6.2 deflating subspaces
2.6.3 equivalences
2.6.4 eigendecompositions
2.6.5 conditioning
2.6.6 specifying an eigenproblem
2.6.7 related eigenproblems
2.6.8 example
2.6.9 singular case
2.7 nonlinear eigenproblems
j. demmel
3 an introduction to iterative projection methods
3.1 introduction
3.2 basic ideas
y. saad
3.3 spectral transformations
r. lehoucq and d. sorensen
4 hermitian eigenvalue problems
4.1 introduction
4.2 direct methods
4.3 single- and multiple-vector iterations
m. gu
4.3.1 power method
4.3.2 inverse iteration
4.3.3 rayleigh quotient iteration
4.3.4 subspace iteration
4.3.5 software availability
4.4 lanczos method
a. ruhe
4.4.1 algorithm
4.4.2 convergence properties
4.4.3 spectral transformation
4.4.4 reorthogonalization
4.4.5 software availability
4.4.6 numerical examples
4.5 implicitly restarted lanczos method
r. lehouc, q and d. sorensen
4.5.1 implicit restart
4.5.2 shift selection
4.5.3 lanczos method in gemv form
4.5.4 convergence properties
4.5.5 computational costs and tradeoffs
4.5.6 deflation and stopping rules
4.5.7 orthogonal deflating transformation
4.5.8 implementation of locking and purging
4.5.9 software availability
4.6 band lanczos method
r. freund
4.6.1 the need for deflation
4.6.2 basic properties
4.6.3 algorithm
4.6.4 variants
4.7 jacobi-davidson methods
g. sleijpen and h. van der vorst
4.7.1 basic theory
4.7.2 basic algorithm
4.7.3 restart and deflation
4.7.4 computing interior eigenvalues
4.7.5 software availability
4.7.6 numerical example
4.8 stability and accuracy assessments
z. bai and r. li
5 generalized hermitian eigenvalue problems
5.1 introduction
5.2 transformation to standard problem
5.3 direct methods
5.4 single- and multiple-vector iterations
m. gu
5.5 lanczos methods
a. ruhe
5.6 jacobi-davidson methods
g. sleijpen and h. van der vorst
5.7 stability and accuracy assessments
z. bai and r. li
5.7.1 positive definite b
5.7.2 some combination of a and b is positive definite
6 singular value decomposition
6.1 introduction
6.2 direct methods
6.3 iterative algorithms
j. demmel
6.3.1 what operations can one afford to perform?
6.3.2 which singular values and vectors are desired?
6.3.3 golub-kahan-lanczos method
6.3.4 software availability
6.3.5 numerical example
6.4 related problems
j. demmel
7 non-hermitian eigenvalue problems
7.1 introduction
7.2 balancing matrices
t. chen and j. demmel
7.2.1 direct balancing
7.2.2 krylov balancing algorithms
7.2.3 accuracy of eigenvalues computed after balancing
7.3 direct methods
7.4 single- and multiple-vector iterations
m. gu
7.4.1 power method
7.4.2 inverse iteration
7.4.3 subspace iteration
7.4.4 software availability
7.5 arnoldi method
y. saad
7.5.1 basic algorithm
7.5.2 variants
7.5.3 explicit restarts
7.5.4 deflation
7.6 implicitly restarted arnoldi method
r. lehoucq and d. sorensen
7.6.1 arnoldi procedure in gemv form
7.6.2 implicit restart
7.6.3 convergence properties
7.6.4 numerical stability
7.6.5 computational costs and tradeoffs
7.6.6 deflation and stopping rules
7.6.7 orthogonal deflating transformation
7.6.8 eigenvector computation with spectral transformation
7.6.9 software availability
7.7 block arnoldi method
r. lehoucq and k. maschhoff
7.7.1 block arnoldi reductions
7.7.2 practical algorithm
7.8 lanczos method
z. bai and d. day
7.8.1 algorithm
7.8.2 convergence properties
7.8.3 software availability
7.8.4 notes and references
7.9 block lanczos methods
z. bai and d. day
7.9.1 basic algorithm
7.9.2 an adaptively blocked lanczos method
7.9.3 software availability
7.9.4 notes and references
7.10 band lanczos method
r. freund
7.10.1 deflation
7.10.2 basic properties
7.10.3 algorithm
7.10.4 application to reduced-order modeling
7.10.5 variants
7.11 lanczos method for complex symmetric eigenproblems
r. freund
7.11.1 properties of complex symmetric matrices
7.11.2 properties of the algorithm
7.11.3 algorithm
7.11.4 solving the reduced eigenvalue problems
7.11.5 software availability
7.11.6 notes and references
7.12 jacobi-davidson methods
g. sleijpen and ii. van der vorst
7.12.1 generalization of hermitian case
7.12.2 schur form and restart
7.12.3 computing interior eigenvalues
7.12.4 software availability
7.12.5 numerical example
7.13 stability and accuracy assessments
z. bai and r. li
8 generalized non-hermitian eigenvalue problems
8.1 introduction
8.2 direct methods
8.3 transformation to standard problems
8.4 jacobi-davidson method
g. sleijpen and h. van der vorst
8.4.1 basic theory
8.4.2 deflation and restart
8.4.3 algorithm
8.4.4 software availability
8.4.5 numerical example
8.5 rational krylov subspace method
a. ruhe
8.6 symmetric indefinite lanczos method
z. bai, t. ericsson, and t. kowalski
8.6.1 some properties of symmetric indefinite matrix pairs
8.6.2 algorithm
8.6.3 stopping criteria and accuracy assessment
8.6.4 singular b
8.6.5 software availability
8.6.6 numerical examples
8.7 singular matrix pencils
b. kagstrom
8.7.1 regular versus singular problems
8.7.2 kronecker canonical form
8.7.3 generic and nongeneric kronecker structures
8.7.4 ill-conditioning
8.7.5 generalized schur-staircase form
8.7.6 guptri algorithm
8.7.7 software availability
8.7.8 more on guptri and numerical examples
8.7.9 notes and references
8.8 stability and accuracy assessments
z. bai and r. li
9 nonlinear eigenvalue problems
9.1 introduction
9.2 quadratic eigenvalue problems
z. bai, g. sleijpen, and ii. van der vorst
9.2.1 introduction
9.2.2 transformation to linear form
9.2.3 spectral transformations for qep
9.2.4 numerical methods for solving linearized problems
9.2.5 jacobi-davidson method
9.2.6 notes and references
9.3 higher order polynomial eigenvalue problems
9.4 nonlinear eigenvalue problems with orthogonality constraints
r. lippert and a. edelman
9.4.1 introduction
9.4.2 matlab templates
9.4.3 sample problems and their differentials
9.4.4 numerical examples
9.4.5 modifying the templates
9.4.6 geometric technicalities
10 common issues
10.1 sparse matrix storage formats
j. dongarra
10.1.1 compressed row storage
10.1.2 compressed column storage
10.1.3 block compressed row storage
10.1.4 compressed diagonal storage
10.1.5 jagged diagonal storage
10.1.6 skyline storage
10.2 matrix-vector and matrix-matrix multiplications
j. dongarra, p. koev, and x. li
10.2.1 blas
10.2.2 sparse blas
10.2.3 fast matrix-vector multiplication for structured matrices
10.3 a brief survey of direct linear solvers
j. demmel, p. koev, and x. li
10.3.1 direct solvers for dense matrices
10.3.2 direct solvers for band matrices
10.3.3 direct solvers for sparse matrices
10.3.4 direct solvers for structured matrices
10.4 a brief survey of iterative linear solvers
h. van der vorst
10.5 parallelism
j. dongarra and x. li
11 preconditioning techniques
11.1 introduction
11.2 inexact methods
k. meerbergen and r. morgan
11.2.1 matrix transformations
11.2.2 inexact matrix transformations
11.2.3 arnoldi method with inexact cayley transform
11.2.4 davidson method
11.2.5 jacobi-davidson method with cayley transform
11.2.6 preconditioned lanczos method
11.2.7 inexact rational krylov method
11.2.8 inexact shift-and-invert
11.3 preconditioned eigensolvers
a. knyazev
11.3.1 introduction
11.3.2 general framework of preconditioning
11.3.3 preconditioned shifted power method
11.3.4 preconditioned steepest ascent/descent methods
11.3.5 preconditioned lanczos methods
11.3.6 davidson method
11.3.7 methods with preconditioned inner iterations
11.3.8 preconditioned conjugate gradient methods
11.3.9 preconditioned simultaneous iterations
11.3.10 software availability
appendix. of things not treated
bibliography
index
list of iterative algorithm templates
list of direct algorithms
list of figures
list of tables
1 introduction
1.1 why eigenvalue templates?
1.2 intended readership
1.3 using the decision tree to choose a template
1.4 what is a template?
1.5 organization of the book
2 a brief tour of eigenproblems
2.1 introduction
2.1.1 numerical stability and conditioning
2.2 hermitian eigenproblems
j. demmel
2.2.1 eigenvalues and eigenvectors
2.2.2 invariant subspaces
2.2.3 equivalences (similarities)
2.2.4 eigendecompositions
2.2.5 conditioning
2.2.6 specifying an eigenproblem
2.2.7 related eigenproblems
2.2.8 example
2.3 generalized hermitian eigenproblems
j. dernrnel
2.3.1 eigenvalues and eigenvectors
2.3.2 eigenspaces
2.3.3 equivalences (congruences)
2.3.4 eigendecompositions
2.3.5 conditioning
2.3.6 specifying an eigenproblem
2.3.7 related eigenproblems
2.3.8 example
2.4 singular value decomposition
j. demrnel
2.4.1 singular values and singular vectors
2.4.2 singular subspaces
2.4.3 equivalences
2.4.4 decompositions
2.4.5 conditioning
2.4.6 specifying a singular value problem
2.4.7 related singular value problems
2.4.8 example
2.5 non-hermitian eigenproblerns
j. demmel
2.5.1 eigenvalues and eigenvectors
2.5.2 invariant subspaces
2.5.3 equivalences (similarities)
2.5.4 eigendecompositions
2.5.5 conditioning
2.5.6 specifying an eigenproblem
2.5.7 related eigenproblems
2.5.8 example
2.6 generalized non-hermitian eigenproblerns
j. demmel
2.6.1 eigenvalues and eigenvectors
2.6.2 deflating subspaces
2.6.3 equivalences
2.6.4 eigendecompositions
2.6.5 conditioning
2.6.6 specifying an eigenproblem
2.6.7 related eigenproblems
2.6.8 example
2.6.9 singular case
2.7 nonlinear eigenproblems
j. demmel
3 an introduction to iterative projection methods
3.1 introduction
3.2 basic ideas
y. saad
3.3 spectral transformations
r. lehoucq and d. sorensen
4 hermitian eigenvalue problems
4.1 introduction
4.2 direct methods
4.3 single- and multiple-vector iterations
m. gu
4.3.1 power method
4.3.2 inverse iteration
4.3.3 rayleigh quotient iteration
4.3.4 subspace iteration
4.3.5 software availability
4.4 lanczos method
a. ruhe
4.4.1 algorithm
4.4.2 convergence properties
4.4.3 spectral transformation
4.4.4 reorthogonalization
4.4.5 software availability
4.4.6 numerical examples
4.5 implicitly restarted lanczos method
r. lehouc, q and d. sorensen
4.5.1 implicit restart
4.5.2 shift selection
4.5.3 lanczos method in gemv form
4.5.4 convergence properties
4.5.5 computational costs and tradeoffs
4.5.6 deflation and stopping rules
4.5.7 orthogonal deflating transformation
4.5.8 implementation of locking and purging
4.5.9 software availability
4.6 band lanczos method
r. freund
4.6.1 the need for deflation
4.6.2 basic properties
4.6.3 algorithm
4.6.4 variants
4.7 jacobi-davidson methods
g. sleijpen and h. van der vorst
4.7.1 basic theory
4.7.2 basic algorithm
4.7.3 restart and deflation
4.7.4 computing interior eigenvalues
4.7.5 software availability
4.7.6 numerical example
4.8 stability and accuracy assessments
z. bai and r. li
5 generalized hermitian eigenvalue problems
5.1 introduction
5.2 transformation to standard problem
5.3 direct methods
5.4 single- and multiple-vector iterations
m. gu
5.5 lanczos methods
a. ruhe
5.6 jacobi-davidson methods
g. sleijpen and h. van der vorst
5.7 stability and accuracy assessments
z. bai and r. li
5.7.1 positive definite b
5.7.2 some combination of a and b is positive definite
6 singular value decomposition
6.1 introduction
6.2 direct methods
6.3 iterative algorithms
j. demmel
6.3.1 what operations can one afford to perform?
6.3.2 which singular values and vectors are desired?
6.3.3 golub-kahan-lanczos method
6.3.4 software availability
6.3.5 numerical example
6.4 related problems
j. demmel
7 non-hermitian eigenvalue problems
7.1 introduction
7.2 balancing matrices
t. chen and j. demmel
7.2.1 direct balancing
7.2.2 krylov balancing algorithms
7.2.3 accuracy of eigenvalues computed after balancing
7.3 direct methods
7.4 single- and multiple-vector iterations
m. gu
7.4.1 power method
7.4.2 inverse iteration
7.4.3 subspace iteration
7.4.4 software availability
7.5 arnoldi method
y. saad
7.5.1 basic algorithm
7.5.2 variants
7.5.3 explicit restarts
7.5.4 deflation
7.6 implicitly restarted arnoldi method
r. lehoucq and d. sorensen
7.6.1 arnoldi procedure in gemv form
7.6.2 implicit restart
7.6.3 convergence properties
7.6.4 numerical stability
7.6.5 computational costs and tradeoffs
7.6.6 deflation and stopping rules
7.6.7 orthogonal deflating transformation
7.6.8 eigenvector computation with spectral transformation
7.6.9 software availability
7.7 block arnoldi method
r. lehoucq and k. maschhoff
7.7.1 block arnoldi reductions
7.7.2 practical algorithm
7.8 lanczos method
z. bai and d. day
7.8.1 algorithm
7.8.2 convergence properties
7.8.3 software availability
7.8.4 notes and references
7.9 block lanczos methods
z. bai and d. day
7.9.1 basic algorithm
7.9.2 an adaptively blocked lanczos method
7.9.3 software availability
7.9.4 notes and references
7.10 band lanczos method
r. freund
7.10.1 deflation
7.10.2 basic properties
7.10.3 algorithm
7.10.4 application to reduced-order modeling
7.10.5 variants
7.11 lanczos method for complex symmetric eigenproblems
r. freund
7.11.1 properties of complex symmetric matrices
7.11.2 properties of the algorithm
7.11.3 algorithm
7.11.4 solving the reduced eigenvalue problems
7.11.5 software availability
7.11.6 notes and references
7.12 jacobi-davidson methods
g. sleijpen and ii. van der vorst
7.12.1 generalization of hermitian case
7.12.2 schur form and restart
7.12.3 computing interior eigenvalues
7.12.4 software availability
7.12.5 numerical example
7.13 stability and accuracy assessments
z. bai and r. li
8 generalized non-hermitian eigenvalue problems
8.1 introduction
8.2 direct methods
8.3 transformation to standard problems
8.4 jacobi-davidson method
g. sleijpen and h. van der vorst
8.4.1 basic theory
8.4.2 deflation and restart
8.4.3 algorithm
8.4.4 software availability
8.4.5 numerical example
8.5 rational krylov subspace method
a. ruhe
8.6 symmetric indefinite lanczos method
z. bai, t. ericsson, and t. kowalski
8.6.1 some properties of symmetric indefinite matrix pairs
8.6.2 algorithm
8.6.3 stopping criteria and accuracy assessment
8.6.4 singular b
8.6.5 software availability
8.6.6 numerical examples
8.7 singular matrix pencils
b. kagstrom
8.7.1 regular versus singular problems
8.7.2 kronecker canonical form
8.7.3 generic and nongeneric kronecker structures
8.7.4 ill-conditioning
8.7.5 generalized schur-staircase form
8.7.6 guptri algorithm
8.7.7 software availability
8.7.8 more on guptri and numerical examples
8.7.9 notes and references
8.8 stability and accuracy assessments
z. bai and r. li
9 nonlinear eigenvalue problems
9.1 introduction
9.2 quadratic eigenvalue problems
z. bai, g. sleijpen, and ii. van der vorst
9.2.1 introduction
9.2.2 transformation to linear form
9.2.3 spectral transformations for qep
9.2.4 numerical methods for solving linearized problems
9.2.5 jacobi-davidson method
9.2.6 notes and references
9.3 higher order polynomial eigenvalue problems
9.4 nonlinear eigenvalue problems with orthogonality constraints
r. lippert and a. edelman
9.4.1 introduction
9.4.2 matlab templates
9.4.3 sample problems and their differentials
9.4.4 numerical examples
9.4.5 modifying the templates
9.4.6 geometric technicalities
10 common issues
10.1 sparse matrix storage formats
j. dongarra
10.1.1 compressed row storage
10.1.2 compressed column storage
10.1.3 block compressed row storage
10.1.4 compressed diagonal storage
10.1.5 jagged diagonal storage
10.1.6 skyline storage
10.2 matrix-vector and matrix-matrix multiplications
j. dongarra, p. koev, and x. li
10.2.1 blas
10.2.2 sparse blas
10.2.3 fast matrix-vector multiplication for structured matrices
10.3 a brief survey of direct linear solvers
j. demmel, p. koev, and x. li
10.3.1 direct solvers for dense matrices
10.3.2 direct solvers for band matrices
10.3.3 direct solvers for sparse matrices
10.3.4 direct solvers for structured matrices
10.4 a brief survey of iterative linear solvers
h. van der vorst
10.5 parallelism
j. dongarra and x. li
11 preconditioning techniques
11.1 introduction
11.2 inexact methods
k. meerbergen and r. morgan
11.2.1 matrix transformations
11.2.2 inexact matrix transformations
11.2.3 arnoldi method with inexact cayley transform
11.2.4 davidson method
11.2.5 jacobi-davidson method with cayley transform
11.2.6 preconditioned lanczos method
11.2.7 inexact rational krylov method
11.2.8 inexact shift-and-invert
11.3 preconditioned eigensolvers
a. knyazev
11.3.1 introduction
11.3.2 general framework of preconditioning
11.3.3 preconditioned shifted power method
11.3.4 preconditioned steepest ascent/descent methods
11.3.5 preconditioned lanczos methods
11.3.6 davidson method
11.3.7 methods with preconditioned inner iterations
11.3.8 preconditioned conjugate gradient methods
11.3.9 preconditioned simultaneous iterations
11.3.10 software availability
appendix. of things not treated
bibliography
index
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