Algorithms for Sparse Linear Systems
Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the c...
שמור ב:
| Main Authors: | , |
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| פורמט: | Online |
| שפה: | אנגלית |
| יצא לאור: |
Springer Nature
2023
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| נושאים: | |
| גישה מקוונת: | ONIX_20230516_9783031258206_22 |
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| _version_ | 1869514446720729088 |
|---|---|
| author | Scott, Jennifer Tůma, Miroslav |
| author_browse | Scott, Jennifer Tůma, Miroslav |
| author_facet | Scott, Jennifer Tůma, Miroslav |
| author_sort | Scott, Jennifer |
| collection | Directory of Open Access Books |
| description | Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics. |
| format | Online |
| id | doab-20.500.12854ir-100188 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1001882024-04-04T14:41:11Z Algorithms for Sparse Linear Systems Scott, Jennifer Tůma, Miroslav Sparse Matrices Algebraic Preconditioners Sparse Direct Methods Incomplete Factorizations Approximate Inverses thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics. 2023-05-17T04:00:45Z 2023-05-17T04:00:45Z 2023-05-16T15:06:16Z 2023 book ONIX_20230516_9783031258206_22 https://library.oapen.org/handle/20.500.12657/62987 9783031258206 9783031258190 https://directory.doabooks.org/handle/20.500.12854/100188 eng Nečas Center Series open access image/jpeg image/jpeg n/a n/a https://library.oapen.org/bitstream/20.500.12657/62987/1/978-3-031-25820-6.pdf https://library.oapen.org/bitstream/20.500.12657/62987/1/978-3-031-25820-6.pdf Springer Nature Birkhäuser 10.1007/978-3-031-25820-6 10.1007/978-3-031-25820-6 9fa3421d-f917-4153-b9ab-fc337c396b5a University of Reading fb471c48-61d1-40b5-a8d7-7abd9278f351 9783031258206 9783031258190 Birkhäuser 242 Cham [...] open access |
| spellingShingle | Sparse Matrices Algebraic Preconditioners Sparse Direct Methods Incomplete Factorizations Approximate Inverses thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists Scott, Jennifer Tůma, Miroslav Algorithms for Sparse Linear Systems |
| title | Algorithms for Sparse Linear Systems |
| title_full | Algorithms for Sparse Linear Systems |
| title_fullStr | Algorithms for Sparse Linear Systems |
| title_full_unstemmed | Algorithms for Sparse Linear Systems |
| title_short | Algorithms for Sparse Linear Systems |
| title_sort | algorithms for sparse linear systems |
| topic | Sparse Matrices Algebraic Preconditioners Sparse Direct Methods Incomplete Factorizations Approximate Inverses thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists |
| topic_facet | Sparse Matrices Algebraic Preconditioners Sparse Direct Methods Incomplete Factorizations Approximate Inverses thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists |
| url | ONIX_20230516_9783031258206_22 |
| work_keys_str_mv | AT scottjennifer algorithmsforsparselinearsystems AT tumamiroslav algorithmsforsparselinearsystems |