Functions of matrices: theory and computation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM, Soc. for Industrial and Applied Math.
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XX, 425 S. Ill., graph. Darst. |
| ISBN: | 9780898716467 |
Internformat
MARC
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| 084 | |a SK 915 |0 (DE-625)143271: |2 rvk | ||
| 084 | |a 15A45 |2 msc | ||
| 084 | |a 65F30 |2 msc | ||
| 084 | |a MAT 150f |2 stub | ||
| 100 | 1 | |a Higham, Nicholas J. |d 1961-2024 |e Verfasser |0 (DE-588)123564441 |4 aut | |
| 245 | 1 | 0 | |a Functions of matrices |b theory and computation |c Nicholas J. Higham |
| 264 | 1 | |a Philadelphia |b SIAM, Soc. for Industrial and Applied Math. |c 2008 | |
| 300 | |a XX, 425 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Matrices |2 gtt | |
| 650 | 7 | |a Matrixfuncties |2 gtt | |
| 650 | 7 | |a Numerieke wiskunde |2 gtt | |
| 650 | 4 | |a Matrices | |
| 650 | 4 | |a Functions | |
| 650 | 4 | |a Factorization (Mathematics) | |
| 650 | 0 | 7 | |a Matrix |g Mathematik |0 (DE-588)4037968-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Matrizenzerlegung |0 (DE-588)4376303-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Matrixfunktion |0 (DE-588)4169117-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Matrix |g Mathematik |0 (DE-588)4037968-1 |D s |
| 689 | 0 | 1 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |D s |
| 689 | 0 | 2 | |a Matrizenzerlegung |0 (DE-588)4376303-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Matrixfunktion |0 (DE-588)4169117-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016430292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016430292 | |
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 220 H638 |
| DE-BY-FWS_katkey | 559486 |
| DE-BY-FWS_media_number | 083000512708 |
| _version_ | 1825993252382179329 |
| adam_text |
Contents
List of Figures
xiii
List of Tables
xv
Preface
xvii
1
Theory of Matrix Functions
1
1.1
Introduction
. 1
1.2
Definitions of
f
(A)
. 2
1.2.1
Jordan Canonical Form
. 2
1.2.2
Polynomial Interpolation
. 4
1.2.3
Cauchy Integral Theorem
. 7
1.2.4
Equivalence of Definitions
. 8
1.2.5
Example: Function of Identity Plus Rank-
1
Matrix
. 8
1.2.6
Example: Function of Discrete Fourier Transform Matrix
. 10
1.3
Properties
. 10
1.4
Nonprimary Matrix Functions
. 14
1.5
Existence of (Real) Matrix Square Roots and Logarithms
. 16
1.6
Classification of Matrix Square Roots and Logarithms
. 17
1.7
Principal Square Root and Logarithm
. 20
1.8
f
{AB)
and
f
(В А).
21
1.9
Miscellany
. 23
1.10
A Brief History of Matrix Functions
. 26
1.11
Notes and References
. 27
Problems
. 29
2
Applications
35
2.1
Differential Equations
. 35
2.1.1
Exponential Integrators
. 36
2.2
Nuclear Magnetic Resonance
. 37
2.3
Markov Models
. 37
2.4
Control Theory
. 39
2.5
The Nonsymmetric Eigenvalue Problem
. 41
2.6
Orthogonalization and the Orthogonal Procrustes Problem
. 42
2.7
Theoretical Particle Physics
. 43
2.8
Other Matrix Functions
. 44
2.9
Nonlinear Matrix Equations
. 44
2.10
Geometric Mean
. 46
2.11
Pseudospectra
. 47
2.12
Algebras
. 47
vii
Contents
2.13
Sensitivity Analysis
. 48
2.14
Other Applications
. 48
2.14.1
Boundary Value Problems
. 48
2.14.2
Semidefinite
Programming
. 48
2.14.3
Matrix Sector Function
. 48
2.14.4
Matrix Disk Function
. 49
2.14.5
The Average Eye in Optics
. 50
2.14.6
Computer Graphics
. 50
2.14.7
Bregman Divergences
. 50
2.14.8
Structured Matrix Interpolation
. 50
2.14.9
The Lambert
W
Function and Delay Differential Equations
. 51
2.15
Notes and References
. 51
Problems
. 52
Conditioning
55
3.1
Condition Numbers
. 55
3.2
Properties of the
Frédiét
Derivative
. 57
3.3
Bounding the Condition Number
. 63
3.4
Computing or Estimating the Condition Number
. 64
3.5
Notes and References
. 69
Problems
. 70
Techniques for General Functions
71
4.1
Matrix Powers
. 71
4.2
Polynomial Evaluation
. 72
4.3
Taylor Series
. 76
4.4
Rational Approximation
. 78
4.4.1
Best
¿(χ
Approximation
. 79
4.4.2
Padé
Approximation
. 79
4.4.3
Evaluating Rational Functions
. 80
4.5
Diagoualization
. 81
4.6 Schur
Decomposition and Triangular Matrices
. 84
4.7
Block Diagonalization
. 89
4.8
Interpolating Polynomial and Characteristic Polynomial
. 89
4.9
Matrix Iterations
. 91
4.9.1
Order of Convergence
. 91
4.9.2
Termination Criteria
. 92
4.9.3
Convergence
. 93
4.9.4
Numerical Stability
. 95
4.10
Preprocessing
. 99
4.11
Bounds for
lì{A)\\
. 102
4.12
Note« and References
. 104
Problems
. 105
Matrix Sign Function
107
5.1
Sensitivity and Conditioning
. 109
5.2 Schur
Method
. 112
5.3
Newton's Method
. 113
5.4
The
Padé
Family of Iterations
. 115
5.5
Scaling the Newton Iteration
. 119
Contents
ix
5.6
Terminating the Iterations
. 121
5.7
Numerical Stability of Sign Iterations
. 123
5.8
Numerical Experiments and Algorithm
. 125
5.9
Best Loo Approximation
. 128
5.10
Notes and References
. 129
Problems
. 131
6
Matrix Square Root
133
6.1
Sensitivity and Conditioning
. 133
6.2 Schur
Method
. 135
6.3
Newton's Method and Its Variants
. 139
6.4
Stability and Limiting Accuracy
. 144
6.4.1
Newton Iteration
. 144
6.4.2
DB
Iterations
. 145
6.4.3
CR Iteration
. 146
6.4.4
IN Iteration
. 146
6.4.5
Summary
. 147
6.5
Scaling the Newton Iteration
. 147
6.6
Numerical Experiments
. 148
6.7
Iterations via the Matrix Sign Function
. 152
6.8
Special Matrices
. 154
6.8.1
Binomial Iteration
. 154
6.8.2
Modified Newton Iterations
. 157
6.8.3
M-Matrices and ff-Matrices
. 159
6.8.4
Hermitian Positive Definite Matrices
. 161
6.9
Computing Small-Normed Square Roots
. 162
6.10
Comparison of Methods
. 164
6.11
Involutory Matrices
. 165
6.12
Notes and References
. 166
Problems
. 168
7
Matrix pth Root
173
7.1
Theory
. 173
7.2 Schur
Method
. 175
7.3
Newton's Method
. 177
7.4
Inverse Newton Method
. 181
7.5 Schur-Newton
Algorithm
. 184
7.6
Matrix Sign Method
. 186
7.7
Notes and References
. 187
Problems
. 189
8
The Polar Decomposition
193
8.1
Approximation Properties
. 197
8.2
Sensitivity and Conditioning
. 199
8.3
Newton's Method
. 202
8.4
Obtaining Iterations via the Matrix Sign Function
. 202
8.5
The
Padé
Family of Methods
. 203
8.6
Scaling the Newton Iteration
. 205
8.7
Terminating the Iterations
. 207
8.8
Numerical Stability and Choice of
Я
. 209
Contents
8.9
Algorithm
.210
8.10
Notes and References
.213
Problems
.216
9
Schur-Parlett Algorithm
221
9.1
Evaluating Functions of the Atomic Blocks
. 221
9.2
Evaluating the Upper Triangular Part of
ƒ
(T)
. 225
9.3
Reordering and Blocking the
Schur Form. 226
9.4
Schur-Parlett Algorithm for
f
(A)
. 228
9.5
Preprocessing
. 230
9.6
Notes and References
. 231
Problems
. 231
10
Matrix Exponential
233
10.1
Basic Properties
. 233
10.2
Conditioning
. 238
10.3
Scaling and Squaring Method
. 241
10.4 Schur
Algorithms
. 250
10.4.1
Newton Divided Difference Interpolation
. 250
10.4.2
Schur-Fréchet
Algorithm
. 251
10.4.3 Schur
Parlett
Algorithm
. 251
10.5
Numerical Experiment
. 252
10.6
Evaluating the
Frédiét
Derivative and Its Norm
. 253
10.6.1
Quadrature
. 254
10.6.2
The
Kronecker
Formulae
. 256
10.6.3
Computing and Estimating the Norm
. 258
10.7
Miscellany
. 259
10.7.1
Hermitian Matrices and Best L^ Approximation
. 259
10.7.2
Essentially
Nonnegative
Matrices
. 260
10.7.3
Preprocessing
. 261
10.7.4
The V' Functions
. 261
10.8
Notes and References
. 262
Problems
. 265
11
Matrix Logarithm
269
11.1
Basic Properties
. 269
11.2
Conditioning
. 272
11.3
Series Expansions
. 273
11.4
Padé
Approximation
. 274
11.5
Inverse Scaling and Squaring Method
. 275
11.5.1 Schur
Decomposition: Triangular Matrices
. 276
11.5.2
Full Matrices
. 278
11.6
Sdiur Algorithms
. 279
11.6.1 Schur
Frédiét
Algorithm
. 279
11.6.2
Schur-Parlett Algorithm
. 279
11.7
Numerical Experiment
. 280
11.8
Evaluating the
Frechei
Derivative
. 281
11.9
Notes and References
. 283
Problems
. 284
Contents
xi
12
Matrix Cosine and Sine
287
12.1
Basic Properties
. 287
12.2
Conditioning
. 289
12.3
Padé
Approximation of Cosine
. 290
12.4
Double Angle Algorithm for Cosine
. 290
12.5
Numerical Experiment
. 295
12.6
Double Angle Algorithm for Sine and Cosine
. 296
12.6.1
Preprocessing
. 299
12.7
Notes and References
. 299
Problems
. 300
13
Function of Matrix Times Vector:
f (A) b
301
13.1
Representation via Polynomial Interpolation
. 301
13.2
Krylov Subspace Methods
. 302
13.2.1
The
Arnoldi
Process
. 302
13.2.2
Arnoldi
Approximation of f(A)b
. 304
13.2.3
Lanczos Biorthogonalization
. 306
13.3
Quadrature
. 306
13.3.1
On the Real Line
. 306
13.3.2
Contour Integration
. 307
13.4
Differential Equations
. 308
13.5
Other Methods
. 309
13.6
Notes and References
. 309
Problems
. 310
14
Miscellany
313
14.1
Structured Matrices
. 313
14.1.1
Algebras and Groups
. 313
14.1.2
Monotone Functions
. 315
14.1.3
Other Structures
. 315
14.1.4
Data Sparse Representations
. 316
14.1.5
Computing Structured /(A) for Structured A
. 316
14.2
Exponential Decay of Functions of Banded Matrices
. 317
14.3
Approximating Entries of Matrix Functions
. 318
A Notation
319
В
Background: Definitions and Useful Pacts
321
B.I Basic Notation
. 321
B.2 Eigenvalues and Jordan Canonical Form
. 321
B.3 Invariant Subspaces
. 323
B.4 Special Classes of Matrices
. 323
B.5 Matrix Factorizations and Decompositions
. 324
B.6
Pseudoinverse
and Orthogonality
. 325
B.6.1
Pseudoinverse
. 325
В.
6.2
Projector and Orthogonal Projector
. 326
B.6.3 Partial Isometry
. 326
B.7 Norms
. 326
B.8 Matrix Sequences and Series
. 328
B.9 Perturbation Expansions for Matrix Inverse
. 328
xii
Contents
8.
10
Sherman-Morrison-Woodbury Formula
. 329
8.
11
Nonnegative
Matrices
. 329
В.
12
Positive (Senii)defmite Ordering
. 330
В.
13
Kroiiecker Product and Sum
. 331
B.14 Sylvester Equation
. 331
B.15 Floating Point Arithmetic
. 331
B.16 Divided Differences
. 332
Problems
.334
С
Operation Counts
335
D
Matrix Function Toolbox
339
Б
Solutions to Problems
343
Bibliography
379
Index
415 |
| adam_txt |
Contents
List of Figures
xiii
List of Tables
xv
Preface
xvii
1
Theory of Matrix Functions
1
1.1
Introduction
. 1
1.2
Definitions of
f
(A)
. 2
1.2.1
Jordan Canonical Form
. 2
1.2.2
Polynomial Interpolation
. 4
1.2.3
Cauchy Integral Theorem
. 7
1.2.4
Equivalence of Definitions
. 8
1.2.5
Example: Function of Identity Plus Rank-
1
Matrix
. 8
1.2.6
Example: Function of Discrete Fourier Transform Matrix
. 10
1.3
Properties
. 10
1.4
Nonprimary Matrix Functions
. 14
1.5
Existence of (Real) Matrix Square Roots and Logarithms
. 16
1.6
Classification of Matrix Square Roots and Logarithms
. 17
1.7
Principal Square Root and Logarithm
. 20
1.8
f
{AB)
and
f
(В А).
21
1.9
Miscellany
. 23
1.10
A Brief History of Matrix Functions
. 26
1.11
Notes and References
. 27
Problems
. 29
2
Applications
35
2.1
Differential Equations
. 35
2.1.1
Exponential Integrators
. 36
2.2
Nuclear Magnetic Resonance
. 37
2.3
Markov Models
. 37
2.4
Control Theory
. 39
2.5
The Nonsymmetric Eigenvalue Problem
. 41
2.6
Orthogonalization and the Orthogonal Procrustes Problem
. 42
2.7
Theoretical Particle Physics
. 43
2.8
Other Matrix Functions
. 44
2.9
Nonlinear Matrix Equations
. 44
2.10
Geometric Mean
. 46
2.11
Pseudospectra
. 47
2.12
Algebras
. 47
vii
Contents
2.13
Sensitivity Analysis
. 48
2.14
Other Applications
. 48
2.14.1
Boundary Value Problems
. 48
2.14.2
Semidefinite
Programming
. 48
2.14.3
Matrix Sector Function
. 48
2.14.4
Matrix Disk Function
. 49
2.14.5
The Average Eye in Optics
. 50
2.14.6
Computer Graphics
. 50
2.14.7
Bregman Divergences
. 50
2.14.8
Structured Matrix Interpolation
. 50
2.14.9
The Lambert
W
Function and Delay Differential Equations
. 51
2.15
Notes and References
. 51
Problems
. 52
Conditioning
55
3.1
Condition Numbers
. 55
3.2
Properties of the
Frédiét
Derivative
. 57
3.3
Bounding the Condition Number
. 63
3.4
Computing or Estimating the Condition Number
. 64
3.5
Notes and References
. 69
Problems
. 70
Techniques for General Functions
71
4.1
Matrix Powers
. 71
4.2
Polynomial Evaluation
. 72
4.3
Taylor Series
. 76
4.4
Rational Approximation
. 78
4.4.1
Best
¿(χ
Approximation
. 79
4.4.2
Padé
Approximation
. 79
4.4.3
Evaluating Rational Functions
. 80
4.5
Diagoualization
. 81
4.6 Schur
Decomposition and Triangular Matrices
. 84
4.7
Block Diagonalization
. 89
4.8
Interpolating Polynomial and Characteristic Polynomial
. 89
4.9
Matrix Iterations
. 91
4.9.1
Order of Convergence
. 91
4.9.2
Termination Criteria
. 92
4.9.3
Convergence
. 93
4.9.4
Numerical Stability
. 95
4.10
Preprocessing
. 99
4.11
Bounds for
lì{A)\\
. 102
4.12
Note« and References
. 104
Problems
. 105
Matrix Sign Function
107
5.1
Sensitivity and Conditioning
. 109
5.2 Schur
Method
. 112
5.3
Newton's Method
. 113
5.4
The
Padé
Family of Iterations
. 115
5.5
Scaling the Newton Iteration
. 119
Contents
ix
5.6
Terminating the Iterations
. 121
5.7
Numerical Stability of Sign Iterations
. 123
5.8
Numerical Experiments and Algorithm
. 125
5.9
Best Loo Approximation
. 128
5.10
Notes and References
. 129
Problems
. 131
6
Matrix Square Root
133
6.1
Sensitivity and Conditioning
. 133
6.2 Schur
Method
. 135
6.3
Newton's Method and Its Variants
. 139
6.4
Stability and Limiting Accuracy
. 144
6.4.1
Newton Iteration
. 144
6.4.2
DB
Iterations
. 145
6.4.3
CR Iteration
. 146
6.4.4
IN Iteration
. 146
6.4.5
Summary
. 147
6.5
Scaling the Newton Iteration
. 147
6.6
Numerical Experiments
. 148
6.7
Iterations via the Matrix Sign Function
. 152
6.8
Special Matrices
. 154
6.8.1
Binomial Iteration
. 154
6.8.2
Modified Newton Iterations
. 157
6.8.3
M-Matrices and ff-Matrices
. 159
6.8.4
Hermitian Positive Definite Matrices
. 161
6.9
Computing Small-Normed Square Roots
. 162
6.10
Comparison of Methods
. 164
6.11
Involutory Matrices
. 165
6.12
Notes and References
. 166
Problems
. 168
7
Matrix pth Root
173
7.1
Theory
. 173
7.2 Schur
Method
. 175
7.3
Newton's Method
. 177
7.4
Inverse Newton Method
. 181
7.5 Schur-Newton
Algorithm
. 184
7.6
Matrix Sign Method
. 186
7.7
Notes and References
. 187
Problems
. 189
8
The Polar Decomposition
193
8.1
Approximation Properties
. 197
8.2
Sensitivity and Conditioning
. 199
8.3
Newton's Method
. 202
8.4
Obtaining Iterations via the Matrix Sign Function
. 202
8.5
The
Padé
Family of Methods
. 203
8.6
Scaling the Newton Iteration
. 205
8.7
Terminating the Iterations
. 207
8.8
Numerical Stability and Choice of
Я
. 209
Contents
8.9
Algorithm
.210
8.10
Notes and References
.213
Problems
.216
9
Schur-Parlett Algorithm
221
9.1
Evaluating Functions of the Atomic Blocks
. 221
9.2
Evaluating the Upper Triangular Part of
ƒ
(T)
. 225
9.3
Reordering and Blocking the
Schur Form. 226
9.4
Schur-Parlett Algorithm for
f
(A)
. 228
9.5
Preprocessing
. 230
9.6
Notes and References
. 231
Problems
. 231
10
Matrix Exponential
233
10.1
Basic Properties
. 233
10.2
Conditioning
. 238
10.3
Scaling and Squaring Method
. 241
10.4 Schur
Algorithms
. 250
10.4.1
Newton Divided Difference Interpolation
. 250
10.4.2
Schur-Fréchet
Algorithm
. 251
10.4.3 Schur
Parlett
Algorithm
. 251
10.5
Numerical Experiment
. 252
10.6
Evaluating the
Frédiét
Derivative and Its Norm
. 253
10.6.1
Quadrature
. 254
10.6.2
The
Kronecker
Formulae
. 256
10.6.3
Computing and Estimating the Norm
. 258
10.7
Miscellany
. 259
10.7.1
Hermitian Matrices and Best L^ Approximation
. 259
10.7.2
Essentially
Nonnegative
Matrices
. 260
10.7.3
Preprocessing
. 261
10.7.4
The V' Functions
. 261
10.8
Notes and References
. 262
Problems
. 265
11
Matrix Logarithm
269
11.1
Basic Properties
. 269
11.2
Conditioning
. 272
11.3
Series Expansions
. 273
11.4
Padé
Approximation
. 274
11.5
Inverse Scaling and Squaring Method
. 275
11.5.1 Schur
Decomposition: Triangular Matrices
. 276
11.5.2
Full Matrices
. 278
11.6
Sdiur Algorithms
. 279
11.6.1 Schur
Frédiét
Algorithm
. 279
11.6.2
Schur-Parlett Algorithm
. 279
11.7
Numerical Experiment
. 280
11.8
Evaluating the
Frechei
Derivative
. 281
11.9
Notes and References
. 283
Problems
. 284
Contents
xi
12
Matrix Cosine and Sine
287
12.1
Basic Properties
. 287
12.2
Conditioning
. 289
12.3
Padé
Approximation of Cosine
. 290
12.4
Double Angle Algorithm for Cosine
. 290
12.5
Numerical Experiment
. 295
12.6
Double Angle Algorithm for Sine and Cosine
. 296
12.6.1
Preprocessing
. 299
12.7
Notes and References
. 299
Problems
. 300
13
Function of Matrix Times Vector:
f (A) b
301
13.1
Representation via Polynomial Interpolation
. 301
13.2
Krylov Subspace Methods
. 302
13.2.1
The
Arnoldi
Process
. 302
13.2.2
Arnoldi
Approximation of f(A)b
. 304
13.2.3
Lanczos Biorthogonalization
. 306
13.3
Quadrature
. 306
13.3.1
On the Real Line
. 306
13.3.2
Contour Integration
. 307
13.4
Differential Equations
. 308
13.5
Other Methods
. 309
13.6
Notes and References
. 309
Problems
. 310
14
Miscellany
313
14.1
Structured Matrices
. 313
14.1.1
Algebras and Groups
. 313
14.1.2
Monotone Functions
. 315
14.1.3
Other Structures
. 315
14.1.4
Data Sparse Representations
. 316
14.1.5
Computing Structured /(A) for Structured A
. 316
14.2
Exponential Decay of Functions of Banded Matrices
. 317
14.3
Approximating Entries of Matrix Functions
. 318
A Notation
319
В
Background: Definitions and Useful Pacts
321
B.I Basic Notation
. 321
B.2 Eigenvalues and Jordan Canonical Form
. 321
B.3 Invariant Subspaces
. 323
B.4 Special Classes of Matrices
. 323
B.5 Matrix Factorizations and Decompositions
. 324
B.6
Pseudoinverse
and Orthogonality
. 325
B.6.1
Pseudoinverse
. 325
В.
6.2
Projector and Orthogonal Projector
. 326
B.6.3 Partial Isometry
. 326
B.7 Norms
. 326
B.8 Matrix Sequences and Series
. 328
B.9 Perturbation Expansions for Matrix Inverse
. 328
xii
Contents
8.
10
Sherman-Morrison-Woodbury Formula
. 329
8.
11
Nonnegative
Matrices
. 329
В.
12
Positive (Senii)defmite Ordering
. 330
В.
13
Kroiiecker Product and Sum
. 331
B.14 Sylvester Equation
. 331
B.15 Floating Point Arithmetic
. 331
B.16 Divided Differences
. 332
Problems
.334
С
Operation Counts
335
D
Matrix Function Toolbox
339
Б
Solutions to Problems
343
Bibliography
379
Index
415 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Higham, Nicholas J. 1961-2024 |
| author_GND | (DE-588)123564441 |
| author_facet | Higham, Nicholas J. 1961-2024 |
| author_role | aut |
| author_sort | Higham, Nicholas J. 1961-2024 |
| author_variant | n j h nj njh |
| building | Verbundindex |
| bvnumber | BV023244812 |
| callnumber-first | Q - Science |
| callnumber-label | QA188 |
| callnumber-raw | QA188 |
| callnumber-search | QA188 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 780 SK 905 SK 220 SK 915 |
| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)268627557 (DE-599)BVBBV023244812 |
| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T20:25:19Z |
| indexdate | 2025-03-08T04:01:06Z |
| institution | BVB |
| isbn | 9780898716467 |
| language | English |
| lccn | 2007061811 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016430292 |
| oclc_num | 268627557 |
| open_access_boolean | |
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| physical | XX, 425 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | SIAM, Soc. for Industrial and Applied Math. |
| record_format | marc |
| spellingShingle | Higham, Nicholas J. 1961-2024 Functions of matrices theory and computation Matrices gtt Matrixfuncties gtt Numerieke wiskunde gtt Matrices Functions Factorization (Mathematics) Matrix Mathematik (DE-588)4037968-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Matrizenzerlegung (DE-588)4376303-0 gnd Matrixfunktion (DE-588)4169117-9 gnd |
| subject_GND | (DE-588)4037968-1 (DE-588)4071510-3 (DE-588)4376303-0 (DE-588)4169117-9 |
| title | Functions of matrices theory and computation |
| title_auth | Functions of matrices theory and computation |
| title_exact_search | Functions of matrices theory and computation |
| title_exact_search_txtP | Functions of matrices theory and computation |
| title_full | Functions of matrices theory and computation Nicholas J. Higham |
| title_fullStr | Functions of matrices theory and computation Nicholas J. Higham |
| title_full_unstemmed | Functions of matrices theory and computation Nicholas J. Higham |
| title_short | Functions of matrices |
| title_sort | functions of matrices theory and computation |
| title_sub | theory and computation |
| topic | Matrices gtt Matrixfuncties gtt Numerieke wiskunde gtt Matrices Functions Factorization (Mathematics) Matrix Mathematik (DE-588)4037968-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Matrizenzerlegung (DE-588)4376303-0 gnd Matrixfunktion (DE-588)4169117-9 gnd |
| topic_facet | Matrices Matrixfuncties Numerieke wiskunde Functions Factorization (Mathematics) Matrix Mathematik Funktion Mathematik Matrizenzerlegung Matrixfunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016430292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT highamnicholasj functionsofmatricestheoryandcomputation |
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