基于圆盘定理的RRQR分解变形  

A variation of RRQR decomposition based on Gershgorin disk theorem

作　　者：贾仲孝[1] 王纪[2] 

机构地区：[1]清华大学数学科学系,北京100084 [2]大连理工大学应用数学系,辽宁大连116024

出　　处：《大连理工大学学报》2004年第2期170-175,共6页Journal of Dalian University of Technology

基　　金：国家重点基础研究专项规划资助项目(G1999032805).

摘　　要：RRQR是确定矩阵的数值秩的一个实用、可靠算法.根据数值秩的定义,基于圆盘定理,改进了主元块(pivotedblocks)算法,在一定条件下能准确找到上三角矩阵的最小奇异值对应的右奇异向量的最大分量位置,从而避免用代价可能很高的反迭代法去计算上三角矩阵的最小奇异值和右奇异向量,数值算例很好地说明了算法的有效性和可靠性.RRQR is a practical and reliable method for determining the numerical rank of a matrix. In terms of the definition of numerical rank, the pivoted block algorithm based on the Gershgorin disk theorem is improved. Under some conditions, the position of the largest absolute value of the elements of the right singular vector corresponding to the smallest singular value of an upper triangular matrix can be exactly found, so the expensive inverse iteration can be avoided. The new algorithm is compared with some existing algorithms. Numerical experiments confirm the reliability of the new algorithm.

关 键 词：圆盘定理 RRQR分解变形 矩阵 数值秩 反主元值 最小奇异值 右奇异向量 

分 类 号：O151.21[理学—数学]