The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=C

The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=C

In this paper, we present two different relaxed gradient based iterative (RGI) algorithms for solving the symmetric and skew symmetric solution of the Sylvester matrix equation AX+XB=C. By using these two iterative methods, it is proved that the iterative solution converges to its true symmetric (sk...

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Main Authors: Xiaodan Zhang, Xingping Sheng
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2017/1624969
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spelling doaj-d7069f4f5d60409ca1966ce3db8e0cb12020-11-25T00:13:51ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472017-01-01201710.1155/2017/16249691624969The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=CXiaodan Zhang0Xingping Sheng1School of Information and Computer, Anhui Agricultural University, Hefei 230036, ChinaSchool of Mathematics and Statistics, Fuyang Normal College, Anhui 236037, ChinaIn this paper, we present two different relaxed gradient based iterative (RGI) algorithms for solving the symmetric and skew symmetric solution of the Sylvester matrix equation AX+XB=C. By using these two iterative methods, it is proved that the iterative solution converges to its true symmetric (skew symmetric) solution under some appropriate assumptions when any initial symmetric (skew symmetric) matrix X0 is taken. Finally, two numerical examples are given to illustrate that the introduced iterative algorithms are more efficient.http://dx.doi.org/10.1155/2017/1624969
collection DOAJ
language English
format Article
sources DOAJ
author Xiaodan Zhang
Xingping Sheng
spellingShingle Xiaodan Zhang
Xingping Sheng
The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=C
Mathematical Problems in Engineering
author_facet Xiaodan Zhang
Xingping Sheng
author_sort Xiaodan Zhang
title The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=C
title_short The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=C
title_full The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=C
title_fullStr The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=C
title_full_unstemmed The Relaxed Gradient Based Iterative Algorithm for the Symmetric (Skew Symmetric) Solution of the Sylvester Equation AX+XB=C
title_sort relaxed gradient based iterative algorithm for the symmetric (skew symmetric) solution of the sylvester equation ax+xb=c
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2017-01-01
description In this paper, we present two different relaxed gradient based iterative (RGI) algorithms for solving the symmetric and skew symmetric solution of the Sylvester matrix equation AX+XB=C. By using these two iterative methods, it is proved that the iterative solution converges to its true symmetric (skew symmetric) solution under some appropriate assumptions when any initial symmetric (skew symmetric) matrix X0 is taken. Finally, two numerical examples are given to illustrate that the introduced iterative algorithms are more efficient.
url http://dx.doi.org/10.1155/2017/1624969
work_keys_str_mv AT xiaodanzhang therelaxedgradientbasediterativealgorithmforthesymmetricskewsymmetricsolutionofthesylvesterequationaxxbc
AT xingpingsheng therelaxedgradientbasediterativealgorithmforthesymmetricskewsymmetricsolutionofthesylvesterequationaxxbc
AT xiaodanzhang relaxedgradientbasediterativealgorithmforthesymmetricskewsymmetricsolutionofthesylvesterequationaxxbc
AT xingpingsheng relaxedgradientbasediterativealgorithmforthesymmetricskewsymmetricsolutionofthesylvesterequationaxxbc
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