五对角矩阵的分解及其逆元素的快速算法

A Fast Algorithm for Inverse of Five-Diagonal Matrices

提出了五对角矩阵的一种分解方法,其运算量比建立在Gaussian消元法基础上的LU方法运算量少,拓广了相应文献的结果,给出了n阶五对角矩阵的扭曲分解式,得到了五对角矩阵逆矩阵元素的快速算法,结果推广到块五对角矩阵。

The algorithm and explicit formulae for the elements of the inverse of five-diagonal matrices are presented. The results are obtained by relationships between the elements of the inverse and the elements of special twisted decompositions of it. Operation count of the algorithm have an advantage over that of the standard LU decomposition based on the Gaussian elimination, and some results can also be extended to block five-diagonal matrices. Result obtained improves result in the known corresponding references.