Adjustment of an inverse matrix corresponding to a change in one element of a given matrix
J Sherman, WJ Morrison - The Annals of Mathematical Statistics, 1950 - JSTOR
J Sherman, WJ Morrison
The Annals of Mathematical Statistics, 1950•JSTOR1. Introduction. Many methods have been published in recent years for carry-ing out the
numerical computation of the inverse of a matrix [1],[2]. In all these methods, the amount of
computation increases rapidly with increase in order of the matrix. The utility of a
computational method for obtaining the inverse of a matrix would be increased considerably
if the inverse could be transformed in a simple manner, corresponding to some specified
change in the original matrix, thus eliminating the necessity of computing the new inverse …
numerical computation of the inverse of a matrix [1],[2]. In all these methods, the amount of
computation increases rapidly with increase in order of the matrix. The utility of a
computational method for obtaining the inverse of a matrix would be increased considerably
if the inverse could be transformed in a simple manner, corresponding to some specified
change in the original matrix, thus eliminating the necessity of computing the new inverse …
1. Introduction. Many methods have been published in recent years for carry-ing out the numerical computation of the inverse of a matrix [1],[2]. In all these methods, the amount of computation increases rapidly with increase in order of the matrix. The utility of a computational method for obtaining the inverse of a matrix would be increased considerably if the inverse could be transformed in a simple manner, corresponding to some specified change in the original matrix, thus eliminating the necessity of computing the new inverse from the beginning. The problem that is considered in the present paper is one of changing one element in the original matrix, and of computing the resulting changes in the elements of the new inverse directly from those of the old inverse.
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