一些结构线性系统的SBE与P-SBE的比较

COMPARING SBE WITH P-SBE FOR CERTAIN STRUCTURED LINEAR SYSTEMS

很多重要的结构矩阵都属于R^n或C^n上纯量积定义的Jordan代数J或者是Lie代数L.本文比较线性系统AX=B关于近似解的范数型结构向后误差(SBE)与偏结构向后误差(P- SBE).这里系数矩阵A∈J或A∈L.在给出若干预备性结果后,先对单右端项情形比较SBE与P-SBE,然后对多右端项情形比较.部分结果是Sun近期的一些结果的推广.

Many important structured matrices belong to the Jordan algebra J or the Lie algebra L, defined by scalar product in R^n or C^n. In this paper, the comparison of normwise structured backward errors （SBE） with partial structured backward errors （P-SBE） with respect to the approximate solution of linear system AX = B are considered. Here the coefficient matrix A satisfies A ∈ J or A ∈ L. After giving some preliminary results, we first compare SBE with P-SBE in case of single right-hand side, then multiple right-hand sides. Some results proved by Sun are generalized.