Inverse Sensitivity Method for Asymmetric Multivariable Nondefective Systems

Abstract

An available parametric correction method for asymmetric multivariable nondefective systems is investigated. It will be proved that the eigensolutions associated with the repeated eigenvalues are not differentiable, although their partial derivatives exist. A calculable generalized Jacobian matrix is presented based on the first-order Taylor expansion of the repeated root eigenpairs as the case of symmetric systems, which ensures the feasibility of the inverse sensitivity method for parametric correction. The first-order directional derivatives of the repeated root eigenpairs are also found. Two numerical asymmetric examples are given to verify the validity of the method by use of simulated data.