Krylov solvers for linear algebraic systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2004
|
| Ausgabe: | 1st ed |
| Schriftenreihe: | Studies in computational mathematics
11 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Includes bibliographical references (p. 315-325) and index The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of the block conjugate-gradient algorithm and it is this observation that permits the unification of the theory. The two major sub-classes of those methods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as natural generalisations of the Orthodir (GCR) and Orthomin algorithms. These are themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt algorithm and their properties, in particular their stability properties, are determined by the two matrices that define the block conjugate-gradient algorithm. These are the matrix of coefficients and the preconditioning matrix. In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms. In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM. Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices. comprehensive and unified approach up-to-date chapter on preconditioners complete theory of stability includes dual and reverse methods comparison of algorithms on CD-ROM objective assessment of algorithms |
| Beschreibung: | 1 Online-Ressource (330 p.) |
| ISBN: | 1423709330 9781423709336 9780444514745 0444514740 0080478875 9780080478876 |
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| 490 | 0 | |a Studies in computational mathematics |v 11 | |
| 500 | |a Includes bibliographical references (p. 315-325) and index | ||
| 500 | |a The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of the block conjugate-gradient algorithm and it is this observation that permits the unification of the theory. The two major sub-classes of those methods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as natural generalisations of the Orthodir (GCR) and Orthomin algorithms. These are themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt algorithm and their properties, in particular their stability properties, are determined by the two matrices that define the block conjugate-gradient algorithm. These are the matrix of coefficients and the preconditioning matrix. In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. | ||
| 500 | |a Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms. In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM. Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. | ||
| 500 | |a Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices. comprehensive and unified approach up-to-date chapter on preconditioners complete theory of stability includes dual and reverse methods comparison of algorithms on CD-ROM objective assessment of algorithms | ||
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Datensatz im Suchindex
| _version_ | 1804152913414586368 |
|---|---|
| any_adam_object | |
| author | Broyden, C. G., (Charles George) |
| author_facet | Broyden, C. G., (Charles George) |
| author_role | aut |
| author_sort | Broyden, C. G., (Charles George) |
| author_variant | c g c g b cgcg cgcgb |
| building | Verbundindex |
| bvnumber | BV042317219 |
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| dewey-full | 512.94 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.94 |
| dewey-search | 512.94 |
| dewey-sort | 3512.94 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
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| isbn | 1423709330 9781423709336 9780444514745 0444514740 0080478875 9780080478876 |
| language | English |
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| spelling | Broyden, C. G., (Charles George) Verfasser aut Krylov solvers for linear algebraic systems by Charles George Broyden, Maria Teresa Vespucci 1st ed Amsterdam Elsevier 2004 1 Online-Ressource (330 p.) txt rdacontent c rdamedia cr rdacarrier Studies in computational mathematics 11 Includes bibliographical references (p. 315-325) and index The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of the block conjugate-gradient algorithm and it is this observation that permits the unification of the theory. The two major sub-classes of those methods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as natural generalisations of the Orthodir (GCR) and Orthomin algorithms. These are themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt algorithm and their properties, in particular their stability properties, are determined by the two matrices that define the block conjugate-gradient algorithm. These are the matrix of coefficients and the preconditioning matrix. In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms. In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM. Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices. comprehensive and unified approach up-to-date chapter on preconditioners complete theory of stability includes dual and reverse methods comparison of algorithms on CD-ROM objective assessment of algorithms MATHEMATICS / Algebra / Elementary bisacsh Algebras, Linear fast Equations / Numerical solutions fast Equations Numerical solutions Algebras, Linear Krylov-Verfahren (DE-588)4425226-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Krylov-Verfahren (DE-588)4425226-2 s 1\p DE-604 Vespucci, M. T. Sonstige oth http://www.sciencedirect.com/science/book/9780444514745 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Broyden, C. G., (Charles George) Krylov solvers for linear algebraic systems MATHEMATICS / Algebra / Elementary bisacsh Algebras, Linear fast Equations / Numerical solutions fast Equations Numerical solutions Algebras, Linear Krylov-Verfahren (DE-588)4425226-2 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4425226-2 (DE-588)4035811-2 |
| title | Krylov solvers for linear algebraic systems |
| title_auth | Krylov solvers for linear algebraic systems |
| title_exact_search | Krylov solvers for linear algebraic systems |
| title_full | Krylov solvers for linear algebraic systems by Charles George Broyden, Maria Teresa Vespucci |
| title_fullStr | Krylov solvers for linear algebraic systems by Charles George Broyden, Maria Teresa Vespucci |
| title_full_unstemmed | Krylov solvers for linear algebraic systems by Charles George Broyden, Maria Teresa Vespucci |
| title_short | Krylov solvers for linear algebraic systems |
| title_sort | krylov solvers for linear algebraic systems |
| topic | MATHEMATICS / Algebra / Elementary bisacsh Algebras, Linear fast Equations / Numerical solutions fast Equations Numerical solutions Algebras, Linear Krylov-Verfahren (DE-588)4425226-2 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | MATHEMATICS / Algebra / Elementary Algebras, Linear Equations / Numerical solutions Equations Numerical solutions Krylov-Verfahren Lineare Algebra |
| url | http://www.sciencedirect.com/science/book/9780444514745 |
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