| 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Tk-1约化到Tk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Tk-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Tk-1关系密切的临时矩阵Hk-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Tk-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. |
| 关键词: Gauss变换 三对角化 矩阵表示 待定元素 递进约化 |
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| A new thought about the reduction method for tridiagonalizing symmetric indefinite matrices |
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SU Er
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College of New Media, Zhejiang Institute of Media and Communications
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| Abstract: |
| The key problem of achievingPAPT=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 determined, and gradual reductions lead to the resultant tridiagonal matrix T. Thus, heavy and tedious matrix correction calculations are avoided. |
| Key words: Gauss transform tridiagonal reduction matrix representation pending element progressive calculation |
