A Theorem on Rank One Modifications to a Matrix and Its Inverse
M. J. D. Powell · The Computer Journal · 1969
Some algorithms need to compute the inverse of the matrix (J + uvT), where J is a non-singular n × n matrix, u and v are n-component column vectors, and where the inverse of J is available. This calculation can be carried out in many ways using only of order n2 computer operations, but if the inverse of J is wrong, then the resultant expression for the inverse of (J + uvT) is usually wrong also. We identify an expression for (J + uvT)−1 that is useful because it tends to suppress the contribution from any errors in J−1.