Developing CRS iterative methods for periodic Sylvester matrix equation
Abstract In this paper, by applying Kronecker product and vectorization operator, we extend two mathematical equivalent forms of the conjugate residual squared (CRS) method to solve the periodic Sylvester matrix equation AjXjBj+CjXj+1Dj=Ejfor j=1,2,…,λ. $$\begin{aligned} A_{j} X_{j} B_{j} + C_{j} X_...
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Online Access: | http://link.springer.com/article/10.1186/s13662-019-2036-1 |
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doaj-cc74f14fb56e40dd88416eb074fc809a2020-11-25T00:06:36ZengSpringerOpenAdvances in Difference Equations1687-18472019-03-012019111110.1186/s13662-019-2036-1Developing CRS iterative methods for periodic Sylvester matrix equationLinjie Chen0Changfeng Ma1College of Mathematics and Informatics, Fujian Normal UniversityCollege of Mathematics and Informatics, Fujian Normal UniversityAbstract In this paper, by applying Kronecker product and vectorization operator, we extend two mathematical equivalent forms of the conjugate residual squared (CRS) method to solve the periodic Sylvester matrix equation AjXjBj+CjXj+1Dj=Ejfor j=1,2,…,λ. $$\begin{aligned} A_{j} X_{j} B_{j} + C_{j} X_{j+1} D_{j} = E_{j} \quad \text{for } j=1,2, \ldots ,\lambda . \end{aligned}$$ We give some numerical examples to compare the accuracy and efficiency of the matrix CRS iterative methods with other methods in the literature. Numerical results validate that the proposed methods are superior to some existing methods and that equivalent mathematical methods can show different numerical performance.http://link.springer.com/article/10.1186/s13662-019-2036-1Conjugate residual squaredIterative methodPeriodic Sylvester matrix equationKronecker productVectorization operator |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Linjie Chen Changfeng Ma |
spellingShingle |
Linjie Chen Changfeng Ma Developing CRS iterative methods for periodic Sylvester matrix equation Advances in Difference Equations Conjugate residual squared Iterative method Periodic Sylvester matrix equation Kronecker product Vectorization operator |
author_facet |
Linjie Chen Changfeng Ma |
author_sort |
Linjie Chen |
title |
Developing CRS iterative methods for periodic Sylvester matrix equation |
title_short |
Developing CRS iterative methods for periodic Sylvester matrix equation |
title_full |
Developing CRS iterative methods for periodic Sylvester matrix equation |
title_fullStr |
Developing CRS iterative methods for periodic Sylvester matrix equation |
title_full_unstemmed |
Developing CRS iterative methods for periodic Sylvester matrix equation |
title_sort |
developing crs iterative methods for periodic sylvester matrix equation |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1847 |
publishDate |
2019-03-01 |
description |
Abstract In this paper, by applying Kronecker product and vectorization operator, we extend two mathematical equivalent forms of the conjugate residual squared (CRS) method to solve the periodic Sylvester matrix equation AjXjBj+CjXj+1Dj=Ejfor j=1,2,…,λ. $$\begin{aligned} A_{j} X_{j} B_{j} + C_{j} X_{j+1} D_{j} = E_{j} \quad \text{for } j=1,2, \ldots ,\lambda . \end{aligned}$$ We give some numerical examples to compare the accuracy and efficiency of the matrix CRS iterative methods with other methods in the literature. Numerical results validate that the proposed methods are superior to some existing methods and that equivalent mathematical methods can show different numerical performance. |
topic |
Conjugate residual squared Iterative method Periodic Sylvester matrix equation Kronecker product Vectorization operator |
url |
http://link.springer.com/article/10.1186/s13662-019-2036-1 |
work_keys_str_mv |
AT linjiechen developingcrsiterativemethodsforperiodicsylvestermatrixequation AT changfengma developingcrsiterativemethodsforperiodicsylvestermatrixequation |
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1725421240726847488 |