Guaranteed accuracy in numerical linear algebra:
Saved in:
| Format: | Book |
|---|---|
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer
1993
|
| Series: | Mathematics and its applications
252 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | XI, 535 S. graph. Darst. |
| ISBN: | 0792323521 |
Staff View
MARC
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| 245 | 1 | 0 | |a Guaranteed accuracy in numerical linear algebra |c by S. K. Godunov ... |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1993 | |
| 300 | |a XI, 535 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics and its applications |v 252 | |
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| 650 | 7 | |a Lineaire algebra |2 gtt | |
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| 650 | 7 | |a Numerieke methoden |2 gtt | |
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| 650 | 7 | |a calcul numérique |2 inriac | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction ix
1 Singular Value Decomposition 1
1.1 Singular Value Decomposition and Singular Values of
Square Matrix 3
1.2 Elementary Orthogonal Transformations 9
1.3 Singular Value Decomposition of Rectangular Matrices . 24
1.4 Norm of Matrix. Singular Values and Singular Vectors . 34
1.5 Some Numerical Characteristics of Matrices 49
1.6 Some Properties of Bidiagonal Square Matrices. Singular
Values and Singular Vectors 58
1.7 Simplification of Matrix Form by Usage of Orthogonal
Transformations 71
1.8 Simplification of Matrix Form by Deflation 86
1.9 Extension of Results for Complex Matrices 98
2 Systems of Linear Equations 109
2.1 Condition Number for Square Matrix Ill
2.2 Systems of Linear Equations with Simplest Band Matri¬
ces of Coefficients 121
2.3 Generalized Normal Solutions of Systems with Arbitrary
Matrices of Coefficients 136
2.4 Conditioning of Generalized Normal Solutions of Sys¬
tems of Full Rank 153
2.5 Angles between Spaces and Their Conditioning 162
vi
2.6 Conditioning of the Generalized Normal Solutions
in Case of Not Full Rank 181
2.7 Generalized Normal r solution of the Systems of Linear
Equations 193
2.8 General Scheme of Finding of r solution of Linear System 207
3 Deflation Algorithms for Band Matrices 215
3.1 Transformations of Hessenberg Matrices by Chains of
Rotations 217
3.2 Deflation of Degenerate Bidiagonal Matrices 235
3.3 Singular Deflation of Non Degenerate Bidiagonal Matrices247
3.4 Spectral Deflation of Hessenbergian and Symmetric
Tridiagonal Matrices 259
3.5 Theory of Perturbations of Singular Deflation of Non
Degenerate Bidiagonal Matrices 267
3.6 Theory of Perturbations of Singular Deflation of Degen¬
erate Bidiagonal Matrices 290
3.7 Theory of Perturbations of Singular Deflation of Sym¬
metric Tridiagonal Matrices 296
4 Sturm Sequences of Tridiagonal Matrices 313
4.1 Elementary Proof of Sturm Theorem 315
4.2 Algorithm of Computation of Eigenvalues of Symmetric
Tridiagonal Matrix 323
4.3 Trigonometric Parametrization of Rational Relations . 336
4.4 Sturm Sequences of Second Kind 349
4.5 One Side Sturm Sequences for Tridiagonal Matrices . . . 355
4.6 Two Side Sturm Sequences for Tridiagonal Symmetric
Matrices 368
4.7 Examples of Calculations in Problems of Finding Eigen¬
values and Sturm Sequences 391
4.8 Two Side Sturm Sequences for Bidiagonal Matrices . . 404
vii
4.9 Examples of Computations of Singular Values and Two
Side Sturm Sequences of Bidiagonal Matrices 417
5 Peculiarities of Computer Computations 425
5.1 Modelling of Errors in Computer Arithmetic Operations 428
5.2 Machine Operations on Vectors and Matrices 443
5.3 Machine Realization of Reflections 452
5.4 Analysis of Errors in Reduction of Matrices into Bi and
Tridiagonal Form 462
5.5 Machine Solution of Systems of Equations with Bidiag¬
onal Coefficient Matrices 471
5.6 Numerical Examples 478
5.7 Machine Realization of Sturm Algorithm. Estimates of
Errors in Computation of Eigenvalues and Singular Values484
5.8 Computation of Two Side Sturm Sequence and Com¬
ponents of Eigenvector of Tridiagonal Symmetric Matrix 493
5.9 Machine Realization of Computations of Two Side
Sturm Sequences for Bidiagonal Matrices 502
5.10 Machine Realization of Deflation Algorithm for
Bidiagonal Matrices 508
Bibliography 523
Index 529
|
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| language | English Russian |
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| spelling | Guaranteed accuracy in numerical linear algebra by S. K. Godunov ... Dordrecht [u.a.] Kluwer 1993 XI, 535 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 252 Aus d. Russ. übers. Analyse vectorielle ram Lineaire algebra gtt MATRICE TRIDIAGONALE inriac Numerieke methoden gtt SYSTEME EQUATION LINEAIRE inriac algèbre linéaire numérique inriac calcul numérique inriac Differential equations, Linear Numerical solutions Vector analysis Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Algorithmus (DE-588)4001183-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Numerische Mathematik (DE-588)4042805-9 s Godunov, Sergej K. Sonstige oth Mathematics and its applications 252 (DE-604)BV008163334 252 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005402699&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Guaranteed accuracy in numerical linear algebra Mathematics and its applications Analyse vectorielle ram Lineaire algebra gtt MATRICE TRIDIAGONALE inriac Numerieke methoden gtt SYSTEME EQUATION LINEAIRE inriac algèbre linéaire numérique inriac calcul numérique inriac Differential equations, Linear Numerical solutions Vector analysis Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4042805-9 (DE-588)4035811-2 (DE-588)4001183-5 |
| title | Guaranteed accuracy in numerical linear algebra |
| title_auth | Guaranteed accuracy in numerical linear algebra |
| title_exact_search | Guaranteed accuracy in numerical linear algebra |
| title_full | Guaranteed accuracy in numerical linear algebra by S. K. Godunov ... |
| title_fullStr | Guaranteed accuracy in numerical linear algebra by S. K. Godunov ... |
| title_full_unstemmed | Guaranteed accuracy in numerical linear algebra by S. K. Godunov ... |
| title_short | Guaranteed accuracy in numerical linear algebra |
| title_sort | guaranteed accuracy in numerical linear algebra |
| topic | Analyse vectorielle ram Lineaire algebra gtt MATRICE TRIDIAGONALE inriac Numerieke methoden gtt SYSTEME EQUATION LINEAIRE inriac algèbre linéaire numérique inriac calcul numérique inriac Differential equations, Linear Numerical solutions Vector analysis Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Lineare Algebra (DE-588)4035811-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Analyse vectorielle Lineaire algebra MATRICE TRIDIAGONALE Numerieke methoden SYSTEME EQUATION LINEAIRE algèbre linéaire numérique calcul numérique Differential equations, Linear Numerical solutions Vector analysis Numerisches Verfahren Numerische Mathematik Lineare Algebra Algorithmus |
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