基于圆盘定理的RRQR分解变形

A variation of RRQR decomposition based on Gershgorin disk theorem

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.