Fast Algorithm for Minimal Polynomial of Matriz and its Application in steepest descent like method

摘要：

Algorithm for the calculation of minimal polynomial of a matrix with complexity of O(m·n2) was proposed, where n is the size of the matrix and m is the degree of the polynomial. The method is based on the further discussion of the relationship between the minimal polynomial of matrix and the minimal polynomial of vector with the matrix. Algorithm for solving system of linear equations whose coefficient matrix is invertible was also presented based on the polynomial with the same complexity, which is a steepest descent like method but its step lengths are the reciprocals of the roots of the polynomial and the exact solution can be theoretically obtained after m steps. The algorithms are efficient when m<<n.

关键词： matriz minimal polynomial eigenvalues steepest descent method system of linear equations

作者: Hongyi Li

作者单位: Shanghai Second Polytechnic University, No.2360, Jin Hai Road, Shanghai, 201209,P.R.China

会议类型: 国际会议

会议名称: The Third International Workshop on Applied Matriz Theory(第三届国际矩阵分析与应用会议)

会议地点: 杭州

会议语种:英文

页码: 589-593

在线出版日期: 2009-07-09（万方平台首次上网日期，不代表论文的发表时间）