A Splitting Iterative Algorithm for Solving Continuous Sylvester Matrix Equations

LI Ying

doi:10.21656/1000-0887.400133

Volume 41 Issue 1

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LI Ying. A Splitting Iterative Algorithm for Solving Continuous Sylvester Matrix Equations[J]. Applied Mathematics and Mechanics, 2020, 41(1): 115-124. doi: 10.21656/1000-0887.400133

Citation:

LI Ying. A Splitting Iterative Algorithm for Solving Continuous Sylvester Matrix Equations[J]. Applied Mathematics and Mechanics, 2020, 41(1): 115-124. doi: 10.21656/1000-0887.400133

Citation:

LI Ying. A Splitting Iterative Algorithm for Solving Continuous Sylvester Matrix Equations[J]. Applied Mathematics and Mechanics, 2020, 41(1): 115-124. doi: 10.21656/1000-0887.400133

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A Splitting Iterative Algorithm for Solving Continuous Sylvester Matrix Equations

doi: 10.21656/1000-0887.400133

LI Ying

School of Information Technology, Shangqiu Normal University,Shangqiu, Henan 476000, P.R.China

Received Date: 2019-04-04
Rev Recd Date: 2019-06-19
Publish Date: 2020-01-01

Abstract

Abstract

The solution of continuous Sylvester matrix equations has significant application value in scientific and engineering calculations, hence, a splitting iterative algorithm was proposed. The core idea of the algorithm is to split the coefficient matrix of the continuous Sylvester matrix equation into a symmetric matrix and an antisymmetric matrix with an outer iterative scheme, and to solve the complex symmetric matrix equation with the inner iterative scheme. Compared with the traditional splitting algorithms, the proposed splitting algorithm effectively avoids the selection of optimal iterative parameters and takes advantages of the efficient solution of complex symmetric equations, which improves the easy implementation and easy operation of the algorithm. In addition, the convergence of the splitting iterative algorithm was further proved theoretically. Numerical examples show that, the splitting iterative algorithm has good convergence and robustness, and the convergence of the splitting iterative algorithm depends on the selection of the inner iterative schemes.
- Sylvester matrix equation,
- complex symmetric matrix equation,
- splitting iterative algorithm,
- convergence

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References

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