Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations
The complexity of open linear algebraic equations makes it difficult to obtain analytical solutions, and preprocessing techniques can be applied to coefficient matrices, which has become an effective method to accelerate the convergence of iterative methods. Therefore, it is important to preprocess...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5435076 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558584237391872 |
|---|---|
| author | Ling Li Yongxian Li |
| author_facet | Ling Li Yongxian Li |
| author_sort | Ling Li |
| collection | DOAJ |
| description | The complexity of open linear algebraic equations makes it difficult to obtain analytical solutions, and preprocessing techniques can be applied to coefficient matrices, which has become an effective method to accelerate the convergence of iterative methods. Therefore, it is important to preprocess the structure of open linear algebraic equations to reduce their complexity. Open linear algebraic equations can be divided into symmetric linear equations and asymmetric linear equations. The former is based on 2 × 2. The latter is preprocessed by the improved QMRGCGS method, and the applications of the two methods are analyzed, respectively. The experimental results show that when the step is 500, the pretreatment time of quasi-minimal residual generalized conjugate gradient square 2 method is 34.23 s, that of conjugate gradient square 2 method is 35.14 s, and that of conjugate gradient square method is 45.20 s, providing a new reference method and idea for solving and preprocessing non-closed linear algebraic equations. |
| format | Article |
| id | doaj-art-4c0d1ff2766e4412ab9528d1a9b44f27 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4c0d1ff2766e4412ab9528d1a9b44f272025-02-03T01:32:03ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5435076Structure Preprocessing Method for the System of Unclosed Linear Algebraic EquationsLing Li0Yongxian Li1School of Mathematics & PhysicsSchool of Mathematics & PhysicsThe complexity of open linear algebraic equations makes it difficult to obtain analytical solutions, and preprocessing techniques can be applied to coefficient matrices, which has become an effective method to accelerate the convergence of iterative methods. Therefore, it is important to preprocess the structure of open linear algebraic equations to reduce their complexity. Open linear algebraic equations can be divided into symmetric linear equations and asymmetric linear equations. The former is based on 2 × 2. The latter is preprocessed by the improved QMRGCGS method, and the applications of the two methods are analyzed, respectively. The experimental results show that when the step is 500, the pretreatment time of quasi-minimal residual generalized conjugate gradient square 2 method is 34.23 s, that of conjugate gradient square 2 method is 35.14 s, and that of conjugate gradient square method is 45.20 s, providing a new reference method and idea for solving and preprocessing non-closed linear algebraic equations.http://dx.doi.org/10.1155/2022/5435076 |
| spellingShingle | Ling Li Yongxian Li Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations Journal of Mathematics |
| title | Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations |
| title_full | Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations |
| title_fullStr | Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations |
| title_full_unstemmed | Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations |
| title_short | Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations |
| title_sort | structure preprocessing method for the system of unclosed linear algebraic equations |
| url | http://dx.doi.org/10.1155/2022/5435076 |
| work_keys_str_mv | AT lingli structurepreprocessingmethodforthesystemofunclosedlinearalgebraicequations AT yongxianli structurepreprocessingmethodforthesystemofunclosedlinearalgebraicequations |