Hilbert Space Splittings and Iterative Methods (Record no. 64773)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04386nam a22005055i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-74370-2 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030113301.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 241107s2024 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031743702 |
| -- | 978-3-031-74370-2 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-74370-2 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA71-90 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBKS |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT041000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBKS |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Griebel, Michael. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 87143 |
| 245 10 - TITLE STATEMENT | |
| Title | Hilbert Space Splittings and Iterative Methods |
| Medium | [electronic resource] / |
| Statement of responsibility, etc. | by Michael Griebel, Peter Oswald. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer Nature Switzerland : |
| -- | Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | IX, 440 p. 1 illus. in color. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Springer Series in Computational Mathematics, |
| International Standard Serial Number | 2198-3712 ; |
| Volume/sequential designation | 62 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1 Introduction -- 2 Hilbert space splittings: Abstract theory -- References -- 3 Hilbert space splittings: Examples and extensions -- References -- 4 Schwarz iterative methods: Finite Omega -- References -- 5 Special topics and extensions -- References -- 6 Schwarz approximation methods: Infinite Omega -- References -- 7 Applications to PDE solvers -- References -- A Hilbert space basics -- A.1 Spaces: Basic notation, definitions and properties -- A.2 Operators between Hilbert spaces -- A.3 Linear equations and variational problems -- A.4 Constructions on Hilbert spaces -- A.5 Sobolev spaces on domains -- A.6 Reproducing kernel Hilbert spaces (RKHS) -- References -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | This book is about the theory of so-called Schwarz methods for solving variational problems in a Hilbert space V arising from linear equations and their associated quadratic minimization problems. Schwarz methods are based on the construction of a sequence of approximate solutions by solving auxiliary variational problems on a set of (smaller, finite-dimensional) Hilbert spaces Vi in a certain order, combining them, and using the combined approximations in an iterative procedure. The spaces Vi form a so-called space splitting for V, they need not necessarily be subspaces of V, and their number can be finite or infinite. The convergence behavior of Schwarz methods is influenced by certain properties of the space splittings they are based on. These properties are identified, and a detailed treatment of traditional deterministic and more recent greedy and stochastic orderings in the subproblem solution process is given, together with an investigation of accelerated methods. To illustrate the abstract theory, the numerical linear algebra analogs of the iterative methods covered in the book are discussed. Its standard application to the convergence theory of multilevel and domain decomposition methods for solving PDE problems is explained, and links to optimization theory and online learning algorithms are given. Providing an introduction and overview of iterative methods which are based on problem decompositions and suitable for parallel and distributed computing, the book could serve as the basis for a one- or two-semester course for M.S. and Ph.D. students specializing in numerical analysis and scientific computing. It will also appeal to a wide range of researchers interested in scientific computing in the broadest sense. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| General subdivision | Data processing. |
| 9 (RLIN) | 65715 |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 66073 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Oswald, Peter. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 87144 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031743696 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031743719 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031743726 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Springer Series in Computational Mathematics, |
| International Standard Serial Number | 2198-3712 ; |
| Volume number/sequential designation | 62 |
| 9 (RLIN) | 87145 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-74370-2">https://doi.org/10.1007/978-3-031-74370-2</a> |
| 912 ## - | |
| -- | ZDB-2-SMA |
| 912 ## - | |
| -- | ZDB-2-SXMS |
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