对称Loewner矩阵Moore-Penrose逆的快速算法

A fast algorithm for the Moore-Penrose inverse of symmetric Loewner matrix

对称Loewner矩阵在自然科学及工程技术中有着广泛的应用,许多问题都归结为求对称Loewner矩阵及其相关矩阵的代数问题.论文通过构造特殊分块矩阵并研究其逆矩阵,给出了秩为n的m×n对称Loewner矩阵Moore-Penrose逆的快速算法,该算法的计算复杂度为O(mn)+O(n2),而通过L+=(LTL)-1LT计算的复杂度为O(mn2)+O(n3).实验数据也表明前者在用时和效率方面均优于后者.

Symmetric Loewner-type matrix has broad applications in natural sciences and engineering technologies.Many of the issues were summarized for the sake of symmetric Loewner（type） matrix and its correlation matrix algebraic problem.This article presented a new fast algorithm of Moore-Penrose inverse for an m×n symmetric Loewner-type matrix with full column rank by forming a special block matrix and studied its inverse.Its computation complexity was O（mn）＋O（n^2）,but it was O（mn^2）＋O（n^3） by using L^＋=（L^TL）^-1L^T.Experimental results also showed that the former in terms of time and accuracy were better than the latter.