求解大型稀疏最小二乘问题的2—块PSD型迭代法

１引言假设Ａ为大型稀疏的ｍ×ｎ实矩阵（ｍ＞ｎ），ｒａｎｋ（Ａ）＝ｎ，在实际中，常常需要求解Ａｘ＝ｂ，（１．１）其中ｂ为给定的ｍ维向量．求（１．１）的欧氏范数最小二乘解等价于求解其中ｒ为ｍ维向量，不失一般性，可令其中Ａ；为ｎ×ｎ满秩方阵，且把ｂ和ｒ也相应地分块为其中ｒ１和ｂ１都是ｎ维向量，用（１．３）和（１．４）的符号，（１．２）可写成等价形式如下相应的块Ｊａｃｏｂｉ迭代矩阵Ｂ２和Ｂ３，定义为Ｃ相应于ＢＬ的分块形式是Ｌ循环阵或是ＧＣＯ（１，Ｌ—１）阵或Ｔ（１，ｌ—１）阵，ＢＬ是指标为Ｌ的弱循环阵（…

2-BLOCK PSD-LIKE ITERATIVE METHODS FOR SOLVING LARGE SPARSE LEAST-SQUARES PROBLEMS

Recently, BSOR BAOR and BSSOR for solving large sparse least-square problems have widely been studied. However, up to now, the optimum 3-BAOR and BSSOR (3-BSSOR and 2-BSSOR) have not been solved. PJ and SSOR are two special schemes of PSD's. In this paper, we have respectively discussed 2-block iterative algorithms for the three iterative methods. Furthermore, their convergent regions, and formulas of their optimum parameters and the corresponding spectral radii are given respectively. Therefore, the difficult problem of the optimum 2-BSSOR has successfuly been settled. It is showed .that BSSOR is an a optimum special scheme of BPSD's in the paper.