A linearized procedure for solving inverse sensitivity equations of non-defective systems

Abstract

A linearized algorithm for solving inverse sensitivity equations of non-defective systems is presented. It is based on the orthonormal decomposition of the first order directional derivatives and directional continuity along τ of the τ−λ base. The least-squares methods which minimize the trace of eigenmode matrix suggested by Pešek and Lallement, respectively, for self-adjoint systems are extended to general non-defective systems in this paper. Moreover, the new algorithm has intuitive simple geometrical significance and is consistent with the first order Taylor expansion of the τ−λ base. The numerical results calculated from the aforementioned three methods are compared, respectively, with the exact solution using two simulation examples. It demonstrates that the results of the proposed algorithm are the nearest to the exact solution.