论文标题
一类用于求解连续sylvester方程的乘法分裂迭代
A class of multiplicative splitting iterations for solving the continuous Sylvester equation
论文作者
论文摘要
为了求解连续的sylvester方程，提出了一类乘法分裂迭代方法。我们考虑了连续Sylvester方程的每个系数矩阵的两个对称正定分组，并且可以等效地将其写成两个乘法分裂矩阵方程。当连续Sylvester方程中的两个系数矩阵都是（非对称）阳性半明确仪时，并且其中至少一个是正定的。我们可以在第一个方程式中选择矩阵$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a和$ b $中偏差。研究了该方法的收敛条件，数值实验显示了该方法的效率。
For solving the continuous Sylvester equation, a class of the multiplicative splitting iteration method is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous Sylvester equations and it can be equivalently written as two multiplicative splitting matrix equations. When both coefficient matrices in the continuous Sylvester equation are (non-symmetric) positive semi-definite, and at least one of them is positive definite; we can choose Hermitian and skew-Hermitian (HS) splittings of matrices $A$ and $B$, in the first equation, and the splitting of the Jacobi iterations for matrices $A$ and $B$, in the second equation in the multiplicative splitting iteration method. Convergence conditions of this method are studied and numerical experiments show the efficiency of this method.
