A new direct method of computing the gradient of the pseudo inverse of a well-conditioned system with respect to a scalar is presented. The proposed method is compared to a $3\times 3$ analytical test case derived using MAPLE. The ability to directly compute the gradient of the pseudo-inverse of a well-conditioned system is examined based on a variety of other test cases, which are not presented in the paper. The results could be of interest for specialists who are using such numerical methods for system sensitivity of a control feedback gain calculation or for structural identification. For this purpose a simple MATLAB code is provided, which could be used for further engineering tools developments.
Reviewer: T.Semerdjiev (Sofia)