n阶方阵A求逆的一个新算法

本文给出了n阶方阵A求逆阵A~(-1)的一个新算法。分解A为A=LU,则A~(-1)=L~(-1)+(I-U)A~(-1)或A~(-1)=U~(-1)+A~(-1)(I—L)。本方法求A~(-1)只用L~(-1)或U~(-1),并当只需要求A~(-1)的部分元素时,特别节省工作量。A对称正定时,分解人为A=LDL~T,我们则有A~(-1)=D_(-1)L~(-1)+(I—L~T)A~(-1)或A~(-1)=L~(-T)D~(-1)+A~(-1)(I-L~T),这较1]不仅减少工作量,而且由于除法运算减少而增加方法的稳定性。

A NEW COMPUTATION OF MATRIX INVERSION

This paper presents a new computation of matrix inversion. It gives out not only the programs but also applied examples.The resolution of A is A=LU, then A~(-I)=L~(-I)+(I-U) A~(-I),or, A~(-I)=U~(-1)+A~(-I)(I-L). when A is positive definite, the resolution of A is A=LDL~T, and then we have A~(-I)=D~(-I)L~(-I)+(I-L~T)A~(-1), or, A~(-I)=L~(-T)D~(-1)+A~(-1)A~(-1)(I-L~T). Compared with the litererature references1], not only is the work load reduced, but also the stability of the computation is increased because of the reduction of division operation.