Milestones in the Development of Iterative Solution Methods
Iterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defect-correction type, commonly referred to as Richardson's iteration method. These methods developed further into various versions of splitting methods, including the succe...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Electrical and Computer Engineering |
| Online Access: | http://dx.doi.org/10.1155/2010/972794 |
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| _version_ | 1841524767044141056 |
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| author | Owe Axelsson |
| author_facet | Owe Axelsson |
| author_sort | Owe Axelsson |
| collection | DOAJ |
| description | Iterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defect-correction type, commonly referred to as Richardson's iteration method. These methods developed further into various versions of splitting methods, including the successive overrelaxation (SOR) method. Later, immensely important developments included convergence acceleration methods, such as the Chebyshev and conjugate gradient iteration methods and preconditioning methods of various forms. A major strive has been to find methods with a total computational complexity of optimal order, that is, proportional to the degrees of freedom involved in the equation. Methods that have turned out to have been particularly important for the further developments of linear equation solvers are surveyed. Some of them are presented in greater detail. |
| format | Article |
| id | doaj-art-1dab8c3ea54d447c89df5e5ffb408057 |
| institution | Kabale University |
| issn | 2090-0147 2090-0155 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Electrical and Computer Engineering |
| spelling | doaj-art-1dab8c3ea54d447c89df5e5ffb4080572025-02-03T05:47:23ZengWileyJournal of Electrical and Computer Engineering2090-01472090-01552010-01-01201010.1155/2010/972794972794Milestones in the Development of Iterative Solution MethodsOwe Axelsson0Institute of Geonics AS CR, 70800 Ostrava, Czech RepublicIterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defect-correction type, commonly referred to as Richardson's iteration method. These methods developed further into various versions of splitting methods, including the successive overrelaxation (SOR) method. Later, immensely important developments included convergence acceleration methods, such as the Chebyshev and conjugate gradient iteration methods and preconditioning methods of various forms. A major strive has been to find methods with a total computational complexity of optimal order, that is, proportional to the degrees of freedom involved in the equation. Methods that have turned out to have been particularly important for the further developments of linear equation solvers are surveyed. Some of them are presented in greater detail.http://dx.doi.org/10.1155/2010/972794 |
| spellingShingle | Owe Axelsson Milestones in the Development of Iterative Solution Methods Journal of Electrical and Computer Engineering |
| title | Milestones in the Development of Iterative Solution Methods |
| title_full | Milestones in the Development of Iterative Solution Methods |
| title_fullStr | Milestones in the Development of Iterative Solution Methods |
| title_full_unstemmed | Milestones in the Development of Iterative Solution Methods |
| title_short | Milestones in the Development of Iterative Solution Methods |
| title_sort | milestones in the development of iterative solution methods |
| url | http://dx.doi.org/10.1155/2010/972794 |
| work_keys_str_mv | AT oweaxelsson milestonesinthedevelopmentofiterativesolutionmethods |