求解多右端对称线性方程组的BMINBACK方法的理论分析与执行

Theoretical analysis and implementation of the BMINBACK method for symmetric linear systems with multiple right-hand sides

研究求解对称多右端线性方程组的极小向后扰动块方法.在块Lanczos执行的过程中采用极小向后扰动范数作为终止算法的条件,对向后扰动的格式及其范数极小值的求法做深入的理论分析,进一步论证了块方法与向后扰动相结合的可行性.通过多组数值实验验证新方法的有效性和优越性..

The minimal backward perturbation block method for solving symmetric linear systems with multiple right-hand sides is studied.The minimal backward perturbation norm is used as the termination condition for the block Lanczos process,the theoretical analysis is discussed on the form of backward perturbation and the method of finding the minimum norm,the feasibility of combining the block process with backward perturbation is further demonstrated.Some numerical experiments are carried out to verify the effectiveness and superiority of the new method.