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.

# A Splitting Iterative Algorithm for Solving Continuous Sylvester Matrix Equations

##### doi: 10.21656/1000-0887.400133
• Received Date: 2019-04-04
• Rev Recd Date: 2019-06-19
• Publish Date: 2020-01-01
• 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.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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