Applied numerical linear algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 419 S. graph. Darst. |
| ISBN: | 9780898713893 0898713897 |
Internformat
MARC
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| 100 | 1 | |a Demmel, James W. |e Verfasser |0 (DE-588)135819067 |4 aut | |
| 245 | 1 | 0 | |a Applied numerical linear algebra |c James W. Demmel |
| 264 | 1 | |a Philadelphia |b SIAM |c 1997 | |
| 300 | |a XII, 419 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Algebras, Linear | |
| 650 | 4 | |a Numerical calculations | |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 1 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007693525&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007693525 | ||
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 915 D382 |
| DE-BY-FWS_katkey | 559485 |
| DE-BY-FWS_media_number | 083000514900 |
| _version_ | 1806177010793316352 |
| adam_text | Contents
Preface
ix
1
Introduction
1
1.1
Basic Notation
........................... 1
1.2
Standard
Problems
of Numerical Linear Algebra
........ 1
1.3
General Techniques
......................... 2
1.3.1
Matrix Factorizations
................... 3
1.3.2
Perturbation Theory and Condition Numbers
...... 4
1.3.3
Effects of Roundoff Error on Algorithms
......... 5
1.3.4
Analyzing the Speed of Algorithms
............ 5
1.3.5
Engineering Numerical Software
............. 6
1.4
Example: Polynomial Evaluation
................. 7
1.5
Floating Point Arithmetic
..................... 9
1.5.1
Further Details
....................... 12
1.6
Polynomial Evaluation Revisited
................. 15
1.7
Vector and Matrix Norms
..................... 19
1.8
References and Other Topics for Chapter
1 ........... 23
1.9
Questions for Chapter
1...................... 24
2
Linear Equation Solving
31
2.1
Introduction
............................. 31
2.2
Perturbation Theory
........................ 32
2.2.1
Relative Perturbation Theory
............... 35
2.3
Gaussian Elimination
........................ 38
2.4
Error Analysis
........................... 44
2.4.1
The Need for Pivoting
................... 45
2.4.2
Formal Error Analysis of Gaussian Elimination
..... 46
2.4.3
Estimating Condition Numbers
.............. 50
2.4.4
Practical Error Bounds
.................. 54
2.5
Improving the Accuracy of a Solution
.............. 60
2.5.1
Single Precision Iterative Refinement
........... 62
2.5.2
Equilibration
........................ 62
2.6
Blocking Algorithms for Higher Performance
.......... 63
2.6.1
Basic Linear Algebra Subroutines
(BLAS)........ 66
2.6.2
How to Optimize Matrix Multiplication
......... 67
2.6.3
Reorganizing Gaussian Elimination to Use Level
3 BLAS 72
2.6.4
More About Parallelism and Other Performance Issues
. 75
2.7
Special
Linear
Systems
....................... 76
2.7.1
Real
Symmetrie
Positive Definite Matrices
........ 76
2.7.2
Symmetric Indefinite Matrices
.............. 79
2.7.3
Band Matrices
....................... 79
2.7.4
General Sparse Matrices
.................. 83
2.7.5
Dense Matrices Depending on Fewer Than 0(n2) Pa¬
rameters
........................... 90
2.8
References and Other Topics for Chapter
2 ........... 93
2.9
Questions for Chapter
2...................... 93
Linear Least Squares Problems
101
3.1
Introduction
............................. 101
3.2
Matrix Factorizations That Solve the Linear Least Squares Prob¬
lem
.................................. 105
3.2.1
Normal Equations
..................... 106
3.2.2
QR Decomposition
..................... 107
3.2.3
Singular Value Decomposition
............... 109
3.3
Perturbation Theory for the Least Squares Problem
...... 117
3.4
Orthogonal Matrices
........................ 118
3.4.1
Householder Transformations
............... 119
3.4.2
Givens
Rotations
...................... 121
3.4.3
Roundoff Error Analysis for Orthogonal Matrices
.... 123
3.4.4
Why Orthogonal Matrices?
................ 124
3.5
Rank-Deficient Least Squares Problems
............. 125
3.5.1
Solving Rank-Deficient Least Squares Problems Using
the
SVD
........................... 128
3.5.2
Solving Rank-Deficient Least Squares Problems Using
QR with Pivoting
..................... 130
3.6
Performance Comparison of Methods for Solving Least Squares
Problems
.............................. 132
3.7
References and Other Topics for Chapter
3 ........... 134
3.8
Questions for Chapter
3...................... 134
Nonsymmetric Eigenvalue Problems
139
4.1
Introduction
............................. 139
4.2
Canonical Forms
.......................... 140
4.2.1
Computing Eigenvectors from the
Schur Form...... 148
4.3
Perturbation Theory
........................ 148
4.4
Algorithms for the Nonsymmetric
Eigenproblem ........ 153
4.4.1
Power Method
....................... 154
4.4.2
Inverse Iteration
...................... 155
4.4.3
Orthogonal Iteration
.................... 156
4.4.4
QR Iteration
........................ 159
4.4.5
Making QR Iteration Practical
.............. 163
4.4.6
Hessenberg
Reduction
................... 164
4.4.7
Tridiagonal
and Bidiagonal
Reduction
.......... 166
4.4.8 QR Iteration
with Implicit Shifts
............. 167
4.5
Other Nonsymmetric Eigenvalue Problems
............ 173
4.5.1
Regular Matrix Pencils and
Weierstrass
Canonical Form
173
4.5.2
Singular Matrix Pencils and the
Kronecker
Canonical Form
....................... 180
4.5.3
Nonlinear Eigenvalue Problems
.............. 183
4.6
Summary
.............................. 184
4.7
References and Other Topics for Chapter
4 ........... 187
4.8
Questions for Chapter
4...................... 187
The Symmetric
Eigenproblem
and Singular Value Decompo¬
sition
195
5.1
Introduction
............................. 195
5.2
Perturbation Theory
........................ 197
5.2.1
Relative Perturbation Theory
............... 207
5.3
Algorithms for the Symmetric
Eigenproblem........... 210
5.3.1
Tridiagonal QR Iteration
................. 212
5.3.2
Rayleigh Quotient Iteration
................ 214
5.3.3
Divide-and-Conquer
.................... 216
5.3.4
Bisection and Inverse Iteration
.............. 228
5.3.5
Jacobi s Method
...................... 232
5.3.6
Performance Comparison
................. 235
5.4
Algorithms for the Singular Value Decomposition
........ 237
5.4.1
QR Iteration and Its Variations for the
Bidiagonal
SVD
242
5.4.2
Computing the
Bidiagonal
SVD
to High Relative Accuracy245
5.4.3
Jacobi s Method for the
SVD
............... 248
5.5
Differential Equations and Eigenvalue Problems
......... 254
5.5.1
The
Toda
Lattice
...................... 255
5.5.2
The Connection to Partial Differential Equations
.... 259
5.6
References and Other Topics for Chapter
5 ........... 260
5.7
Questions for Chapter
5...................... 260
Iterative Methods for Linear Systems
265
6.1
Introduction
............................. 265
6.2
On-line Help for Iterative Methods
................ 266
6.3
Poisson s Equation
......................... 267
6.3.1
Poisson s Equation in One Dimension
.......... 267
6.3.2
Poisson s Equation in Two Dimensions
.......... 270
6.3.3
Expressing Poisson s Equation with
Kronecker
Products
274
6.4
Summary of Methods for Solving Poisson s Equation
...... 277
6.5
Basic Iterative Methods
...................... 279
6.5.1
Jacobi s Method
...................... 281
6.5.2
Gauss-Seidel Method
................... 282
6.5.3
Successive Overrelaxation
................. 283
6.5.4
Convergence
of Jacobi s, Gauss-Seidel, and
SOR^) Methods on the Model Problem
......... 285
6.5.5
Detailed Convergence Criteria for Jacobi s,
Gauss-Seidel, and
SOR(w)
Methods
........... 286
6.5.6
Chebyshev Acceleration and Symmetric
SOR (SSOR)
. 294
6.6
Krylov Subspace Methods
..................... 299
6.6.1
Extracting Information about A via Matrix-Vector Mul¬
tiplication
.......................... 301
6.6.2
Solving Ax
=
b
Using the Krylov Subspace JCk
..... 305
6.6.3
Conjugate Gradient Method
................ 307
6.6.4
Convergence Analysis of the Conjugate Gradient Method
312
6.6.5
Preconditioning
....................... 316
6.6.6
Other Krylov Subspace Algorithms for Solving Ax
=
b
. 319
6.7
Fast Fourier Transform
....................... 321
6.7.1
The Discrete Fourier Transform
.............. 323
6.7.2
Solving the Continuous Model Problem Using Fourier
Series
............................ 324
6.7.3
Convolutions
........................ 325
6.7.4
Computing the Fast Fourier Transform
.......... 326
6.8
Block Cyclic Reduction
...................... 327
6.9
Multigrid
.............................. 331
6.9.1
Overview of Multigrid on the Two-Dimensional Poisson s
Equation
.......................... 332
6.9.2
Detailed Description of Multigrid on the One-Dimensional
Poisson s Equation
..................... 337
6.10
Domain Decomposition
...................... 347
6.10.1
Nonoverlapping
Methods
................. 348
6.10.2
Overlapping Methods
................... 351
6.11
References and Other Topics for Chapter
6 ........... 356
6.12
Questions for Chapter
6...................... 356
7
Iterative Methods for Eigenvalue Problems
361
7.1
Introduction
............................. 361
7.2
The Rayleigh-Ritz Method
.................... 362
7.3
The Lanczos Algorithm in Exact Arithmetic
........... 366
7.4
The Lanczos Algorithm in Floating Point Arithmetic
...... 375
7.5
The Lanczos Algorithm with Selective Orthogonalization
.... 382
7.6
Beyond Selective Orthogonalization
................ 383
7.7
Iterative Algorithms for the Nonsymmetric
Eigenproblem . . . 384
7.8
References and Other Topics for Chapter
7 ........... 386
7.9
Questions for Chapter
7...................... 386
Bibliography
389
Index
409
|
| any_adam_object | 1 |
| author | Demmel, James W. |
| author_GND | (DE-588)135819067 |
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| author_role | aut |
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| callnumber-label | QA184 |
| callnumber-raw | QA184.D455 1997 |
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| callnumber-sort | QA 3184 D455 41997 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 220 SK 915 |
| classification_tum | MAT 657f |
| ctrlnum | (OCoLC)263923609 (DE-599)BVBBV011439402 |
| dewey-full | 512.5 512/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 512/.5 |
| dewey-search | 512.5 512/.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011439402 |
| illustrated | Illustrated |
| indexdate | 2024-08-01T11:30:25Z |
| institution | BVB |
| isbn | 9780898713893 0898713897 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007693525 |
| oclc_num | 263923609 |
| open_access_boolean | |
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| physical | XII, 419 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | SIAM |
| record_format | marc |
| spellingShingle | Demmel, James W. Applied numerical linear algebra Algebras, Linear Numerical calculations Lineare Algebra (DE-588)4035811-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4128130-5 |
| title | Applied numerical linear algebra |
| title_auth | Applied numerical linear algebra |
| title_exact_search | Applied numerical linear algebra |
| title_full | Applied numerical linear algebra James W. Demmel |
| title_fullStr | Applied numerical linear algebra James W. Demmel |
| title_full_unstemmed | Applied numerical linear algebra James W. Demmel |
| title_short | Applied numerical linear algebra |
| title_sort | applied numerical linear algebra |
| topic | Algebras, Linear Numerical calculations Lineare Algebra (DE-588)4035811-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Algebras, Linear Numerical calculations Lineare Algebra Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007693525&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT demmeljamesw appliednumericallinearalgebra |
Inhaltsverzeichnis
Schweinfurt Zentralbibliothek Lesesaal
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2000 SK 915 D382 |
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