一类复对称线性方程组的块三角分裂及其预处理迭代算法

Block triangular splitting and its preconditioning iterative algorithms for a class of complex symmetric linear systems

基于2×2块矩阵的块三角分裂,提出求解复对称线性方程组的块三角分裂(BTS)迭代方法及其预处理迭代方法(PBTS)。理论分析表明,在迭代参数α满足一定的条件下,BTS和PBTS迭代方法是收敛性的,给出两类方法迭代格式中理论最优参数的计算方法。数值实验结果证明BTS迭代方法和PBTS迭代方法的有效性和优越性。

Based on block triangular splitting for block 2×2 matrix,the block triangular splitting(BTS)iteration method and the preconditioned block triangular splitting(PBTS)iteration method for a class of complex symmetric linear system are proposed.Theoretical analysis shows that the BTS and PBTS methods converge under certain conditions.The optimal iteration parameters of these two methods are obtained.Numerical experiments demonstrate the effectiveness and superiority of the BTS method and the PBTS iterative methods.