Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle
This paper is concerned with iterative solution to a class of the real coupled matrix equations. By using the hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled matrix equations A1XB1+A2XB2=F1 and C1XD1+C2XD2=F2. The range of the conv...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/649524 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562021389828096 |
|---|---|
| author | Huamin Zhang |
| author_facet | Huamin Zhang |
| author_sort | Huamin Zhang |
| collection | DOAJ |
| description | This paper is concerned with iterative solution to a class of the real coupled matrix equations. By using the
hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled
matrix equations A1XB1+A2XB2=F1 and C1XD1+C2XD2=F2. The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value. The analysis indicates that
if the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact one
for any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness of
the proposed algorithm. |
| format | Article |
| id | doaj-art-f09bd8706a214020be248041ca4fe0b3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f09bd8706a214020be248041ca4fe0b32025-02-03T01:23:45ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/649524649524Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification PrincipleHuamin Zhang0Department of Mathematics and Physics, Bengbu College, Bengbu 233030, ChinaThis paper is concerned with iterative solution to a class of the real coupled matrix equations. By using the hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled matrix equations A1XB1+A2XB2=F1 and C1XD1+C2XD2=F2. The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value. The analysis indicates that if the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact one for any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness of the proposed algorithm.http://dx.doi.org/10.1155/2014/649524 |
| spellingShingle | Huamin Zhang Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle Abstract and Applied Analysis |
| title | Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle |
| title_full | Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle |
| title_fullStr | Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle |
| title_full_unstemmed | Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle |
| title_short | Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle |
| title_sort | iterative solutions of a set of matrix equations by using the hierarchical identification principle |
| url | http://dx.doi.org/10.1155/2014/649524 |
| work_keys_str_mv | AT huaminzhang iterativesolutionsofasetofmatrixequationsbyusingthehierarchicalidentificationprinciple |