Developing BiCOR and CORS methods for coupled Sylvester-transpose and periodic Sylvester matrix equations
Developing BiCOR and CORS methods for coupled Sylvester-transpose and periodic Sylvester matrix equations
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DOI：
10.1016/j.apm.2015.01.026
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发表时间：
2015-10
影响因子：
5
通讯作者：
M. Hajarian
中科院分区：
文献类型：
--
作者：
M. Hajarian
近年来，双共轭A-正交残差（BiCOR）和共轭A-正交残差平方（CORS）方法被引入求解非对称线性方程组Ax=B.本文直接发展了BiCOR和CORS方法，得到了求解耦合Sylvester转置矩阵方程∑k= 1 l的矩阵迭代方法（A1，kXB 1，k+C1，kXTD 1，k+E1，kYF 1，k）=M1，∑k=1l（A2，kXB 2，k+C2，kXTD 2，k+E2，kYF 2，k）=M2，以及耦合周期西尔维斯特矩阵方程A1，jXjB 1，j+C1，jXj+1D 1，j+E1，jYjF 1，j=M1，j，A2，jXjB 2，j+C2，jXj+1D 2，j+ E_2，jYjF_2，j= M_2，j，其中j = 1，2，…，μ.文末给出了数值例子，比较了矩阵迭代法与文献中其它方法的精度和效率.
Recently the biconjugate A-orthogonal residual (BiCOR) and the conjugate A-orthogonal residual squared (CORS) methods have been introduced for solving nonsymmetric linear systems Ax=b. This study directly develops the BiCOR and CORS methods to obtain matrix iterative methods for solving the coupled Sylvester-transpose matrix equations∑k=1l(A1,kXB1,k+C1,kXTD1,k+E1,kYF1,k)=M1,∑k=1l(A2,kXB2,k+C2,kXTD2,k+E2,kYF2,k)=M2,and the coupled periodic Sylvester matrix equationsA1,jXjB1,j+C1,jXj+1D1,j+E1,jYjF1,j=M1,j,A2,jXjB2,j+C2,jXj+1D2,j+E2,jYjF2,j=M2,j,forj=1,2,…,μ.Numerical examples are given at the end of this paper to compare the accuracy and efficiency of the matrix iterative methods with other methods in the literature.