Spectral computations for bounded operators:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2001
|
| Series: | Applied mathematics and mathematical computation
18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 382 S. graph. Darst. |
| ISBN: | 1584881968 |
Staff View
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Record in the Search Index
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| adam_text | SPECTRAL COMPUTATIONS FOR BOUNDED OPERATORS MARIO AHUES ALAIN LARGILLIER
BALMOHAN V. LIMAYE CHAPMAN & HALL/CRC BOCA RATON LONDON NEW YORK
WASHINGTON, D.C. CONTENTS PREFACE IX NOTATION XIII 1 SPECTRAL
DECOMPOSITION 1 1.1 GENERAL NOTIONS 1 1.2 DECOMPOSITIONS 21 1.3 SPECTRAL
SETS OF FINITE TYPE 33 1.4 ADJOINT AND PRODUCT SPACES 41 1.4.1 ADJOINT
SPACE 41 1.4.2 PRODUCT SPACE 48 1.5 EXERCISES 64 2 SPECTRAL
APPROXIMATION 69 2.1 CONVERGENCE OF OPERATORS 69 2.2 PROPERTY U 76 2.3
PROPERTY L 81 2.4 ERROR ESTIMATES 90 2.5 EXERCISES 106 3 IMPROVEMENT OF
ACCURACY 113 3.1 ITERATIVE REFINEMENT 114 3.1.1 GENERAL REMARKS 114
3.1.2 REFINEMENT SCHEMES FOR A SIMPLE EIGENVALUE ... 119 3.1.3
REFINEMENT SCHEMES FOR A CLUSTER OF EIGENVALUES . 134 3.2 ACCELERATION
148 3.2.1 MOTIVATION 148 3.2.2 HIGHER ORDER SPECTRAL APPROXIMATION 156
VI 3.2.3 SIMPLE EIGENVALUE AND CLUSTER OF EIGENVALUES . . . 162 3.2.4
DEPENDENCE ON THE ORDER OF THE SPECTRAL ANALYSIS 176 3.3 EXERCISES 181
FINITE RANK APPROXIMATIONS 185 4.1 APPROXIMATIONS BASED ON PROJECTIONS
185 4.1.1 TRUNCATION OF A SCHAUDER EXPANSION 187 4.1.2 INTERPOLATORY
PROJECTIONS 190 4.1.3 ORTHOGONAL PROJECTIONS ON SUBSPACES OF PIECEWISE
CONSTANT FUNCTIONS 195 4.1.4 FINITE ELEMENT APPROXIMATION 197 4.2
APPROXIMATIONS OF INTEGRAL OPERATORS 199 4.2.1 DEGENERATE KERNEL
APPROXIMATION 200 4.2.2 APPROXIMATIONS BASED ON NUMERICAL INTEGRATION .
203 4.2.3 WEAKLY SINGULAR INTEGRAL OPERATORS 222 4.3 A POSTERIORI ERROR
ESTIMATES 230 4.4 EXERCISES 240 MATRIX FORMULATIONS 247 5.1 FINITE RANK
OPERATORS 248 5.1.1 SINGULARITY SUBTRACTION 257 5.1.2 UNIFORMLY
WELL-CONDITIONED BASES 264 5.2 ITERATIVE REFINEMENT 275 5.3 ACCELERATION
282 5.4 NUMERICAL EXAMPLES 300 5.5 EXERCISES 309 MATRIX COMPUTATIONS 315
6.1 QR FACTORIZATION 316 6.1.1 HOUSEHOLDER SYMMETRIES 319 6.1.2
HESSENBERG MATRICES 324 6.2 CONVERGENCE OF A SEQUENCE OF SUBSPACES 327
6.2.1 BASIC DEFINITIONS 327 6.2.2 KRYLOV SEQUENCES 331 6.3 QR METHODS
AND INVERSE ITERATION 336 6.3.1 THE FRANCIS-KUBLANOVSKAYA QR METHOD 336
6.3.2 SIMULTANEOUS INVERSE ITERATION METHOD 342 6.4 ERROR ANALYSIS 344
6.4.1 CONDITION NUMBERS OR FORWARD ERROR ANALYSIS . . 344 6.4.2
STABILITY OR BACKWARD ERROR ANALYSIS 347 VLL 6.4.3 RELATIVE ERROR IN
SPECTRAL COMPUTATIONS AND STOPPING CRITERIA FOR THE BASIC QR METHOD ....
362 6.4.4 RELATIVE ERROR IN SOLVING A SYLVESTER EQUATION . . 369
REFERENCES 373 INDEX 379
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:58Z |
| institution | BVB |
| isbn | 1584881968 |
| language | English |
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| physical | XVII, 382 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Applied mathematics and mathematical computation |
| series2 | Applied mathematics and mathematical computation |
| spelling | Ahueś, Mario Verfasser aut Spectral computations for bounded operators Mario Ahues ; Alain Largillier ; Balmohan V. Limaye Boca Raton [u.a.] Chapman & Hall/CRC 2001 XVII, 382 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematics and mathematical computation 18 Eigenwaarden gtt Operatortheorie gtt Opérateurs, Théorie des Spectraaltheorie gtt Spectre (Mathématiques) Operator theory Spectral theory (Mathematics) Beschränkter Operator (DE-588)4233452-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Beschränkter Operator (DE-588)4233452-4 s Spektraltheorie (DE-588)4116561-5 s DE-604 Limaye, Balmohan Vishnu Verfasser (DE-588)124104622 aut Largillier, Alain Verfasser aut Applied mathematics and mathematical computation 18 (DE-604)BV006188231 18 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009547136&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ahueś, Mario Limaye, Balmohan Vishnu Largillier, Alain Spectral computations for bounded operators Applied mathematics and mathematical computation Eigenwaarden gtt Operatortheorie gtt Opérateurs, Théorie des Spectraaltheorie gtt Spectre (Mathématiques) Operator theory Spectral theory (Mathematics) Beschränkter Operator (DE-588)4233452-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4233452-4 (DE-588)4116561-5 |
| title | Spectral computations for bounded operators |
| title_auth | Spectral computations for bounded operators |
| title_exact_search | Spectral computations for bounded operators |
| title_full | Spectral computations for bounded operators Mario Ahues ; Alain Largillier ; Balmohan V. Limaye |
| title_fullStr | Spectral computations for bounded operators Mario Ahues ; Alain Largillier ; Balmohan V. Limaye |
| title_full_unstemmed | Spectral computations for bounded operators Mario Ahues ; Alain Largillier ; Balmohan V. Limaye |
| title_short | Spectral computations for bounded operators |
| title_sort | spectral computations for bounded operators |
| topic | Eigenwaarden gtt Operatortheorie gtt Opérateurs, Théorie des Spectraaltheorie gtt Spectre (Mathématiques) Operator theory Spectral theory (Mathematics) Beschränkter Operator (DE-588)4233452-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Eigenwaarden Operatortheorie Opérateurs, Théorie des Spectraaltheorie Spectre (Mathématiques) Operator theory Spectral theory (Mathematics) Beschränkter Operator Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009547136&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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