Iterative Solution of Large Sparse Systems of Equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1994
|
| Series: | Applied Mathematical Sciences
95 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | C. F. Gauß in a letter from Dec. 26, 1823 to Gerling: Ich empfehle Ihnen diesen Modus zur Nachahmung. Schwerlich werden Sie je wieder direct eliminiren, wenigstens nicht, wenn sie mehr als 2 Unbekannte haben. Das indirecte Verfahren lässt sich halb im Schlafe ausführen, oder man kann während desselben an andere Dinge denken. [C. F. Gauß: Werke vol. 9, Göttingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student of linear algebra are applicable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algorithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e. , they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equations, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics |
| Physical Description: | 1 Online-Ressource (XXII, 432 p) |
| ISBN: | 9781461242888 9781461287247 |
| DOI: | 10.1007/978-1-4612-4288-8 |
Staff View
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| spelling | Hackbusch, Wolfgang 1948- Verfasser (DE-588)115588582 aut Iterative Solution of Large Sparse Systems of Equations by Wolfgang Hackbusch New York, NY Springer New York 1994 1 Online-Ressource (XXII, 432 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 95 C. F. Gauß in a letter from Dec. 26, 1823 to Gerling: Ich empfehle Ihnen diesen Modus zur Nachahmung. Schwerlich werden Sie je wieder direct eliminiren, wenigstens nicht, wenn sie mehr als 2 Unbekannte haben. Das indirecte Verfahren lässt sich halb im Schlafe ausführen, oder man kann während desselben an andere Dinge denken. [C. F. Gauß: Werke vol. 9, Göttingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student of linear algebra are applicable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algorithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e. , they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equations, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics Mathematics Numerical analysis Numerical Analysis Mathematik Programm (DE-588)4047394-6 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf PASCAL Programmiersprache (DE-588)4044804-6 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Schwach besetzte Matrix (DE-588)4056053-3 gnd rswk-swf Gleichungssystem (DE-588)4128766-6 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Schwach besetzte Matrix (DE-588)4056053-3 s Iteration (DE-588)4123457-1 s Numerisches Verfahren (DE-588)4128130-5 s Programm (DE-588)4047394-6 s Gleichungssystem (DE-588)4128766-6 s 2\p DE-604 PASCAL Programmiersprache (DE-588)4044804-6 s 3\p DE-604 Applied Mathematical Sciences 95 (DE-604)BV040244599 95 https://doi.org/10.1007/978-1-4612-4288-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hackbusch, Wolfgang 1948- Iterative Solution of Large Sparse Systems of Equations Applied Mathematical Sciences Mathematics Numerical analysis Numerical Analysis Mathematik Programm (DE-588)4047394-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd PASCAL Programmiersprache (DE-588)4044804-6 gnd Iteration (DE-588)4123457-1 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd Gleichungssystem (DE-588)4128766-6 gnd |
| subject_GND | (DE-588)4047394-6 (DE-588)4128130-5 (DE-588)4044804-6 (DE-588)4123457-1 (DE-588)4056053-3 (DE-588)4128766-6 (DE-588)4113937-9 |
| title | Iterative Solution of Large Sparse Systems of Equations |
| title_auth | Iterative Solution of Large Sparse Systems of Equations |
| title_exact_search | Iterative Solution of Large Sparse Systems of Equations |
| title_full | Iterative Solution of Large Sparse Systems of Equations by Wolfgang Hackbusch |
| title_fullStr | Iterative Solution of Large Sparse Systems of Equations by Wolfgang Hackbusch |
| title_full_unstemmed | Iterative Solution of Large Sparse Systems of Equations by Wolfgang Hackbusch |
| title_short | Iterative Solution of Large Sparse Systems of Equations |
| title_sort | iterative solution of large sparse systems of equations |
| topic | Mathematics Numerical analysis Numerical Analysis Mathematik Programm (DE-588)4047394-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd PASCAL Programmiersprache (DE-588)4044804-6 gnd Iteration (DE-588)4123457-1 gnd Schwach besetzte Matrix (DE-588)4056053-3 gnd Gleichungssystem (DE-588)4128766-6 gnd |
| topic_facet | Mathematics Numerical analysis Numerical Analysis Mathematik Programm Numerisches Verfahren PASCAL Programmiersprache Iteration Schwach besetzte Matrix Gleichungssystem Hochschulschrift |
| url | https://doi.org/10.1007/978-1-4612-4288-8 |
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