对称不定矩阵三对角化约化方法的新讨论  

A new thought about the reduction method for tridiagonalizing symmetric indefinite matrices

作　　者：苏尔[1] 

机构地区：[1]浙江传媒学院新媒体学院,杭州310018

出　　处：《上海师范大学学报（自然科学版）》2013年第6期584-594,共11页Journal of Shanghai Normal University(Natural Sciences)

摘　　要：对称不定矩阵实现三对角分解PAPT=LTLT的关键问题是如何从T k-1约化到T k进行递推计算,直接计算的工作量很大.用构造兼证明方法实现对称三对角阵T k-1矩阵表示的递进约化,在利用Gauss变换的乘积性质容易确定单位下三角阵的递推基础上,建立一个与T k-1关系密切的临时矩阵H k-1为纽带,以矩阵关系确定的元素关系运算操作为推进依据,以矩阵表示的待定元素为直接运算结果,确定T k-1矩阵表示的递进过程,逐步约化得最终的矩阵三对角化结果 T,从而代替矩阵本身繁琐的直接运算.The key problem of achieving PAPT = LTLT for tridiagonalizing symmetric indefinite matrices is how to design the recurrence calculations from Tk-1 to Tk. Direct calculations would lead to a heavy workload. With construction and proof, this paper studies the progressive reduction. Using the multiplication property of the Gauss transform, we can easily determine the recursion of unit lower triangular matrices. Thus, we establish a temporary matrix Hk-1 which is closely related to Tk-1. Element relations reflect the operation process and pending elements will provide the result. Then, with Tk-1, the progressive process is deter- mined, and gradual reductions lead to the resultant tridiagonal matrix T. Thus, heavy and tedious matrix correction calculations are avoided.

关 键 词：Gauss变换 三对角化 矩阵表示 待定元素 递进约化 

分 类 号：O241.6[理学—计算数学]