An Ulm-Like Cayley Transform Method for Inverse Eigenvalue Problems with Multiple Eigenvalues

Abstract

We study the convergence of an Ulm-like Cayley transform method for solving inverse eigenvalue problems which avoids solving approximate Jacobian equations. Under the nonsingularity assumption of the relative generalized Jacobian matrices at the solution, a convergence analysis covering both the distinct and multiple eigenvalues cases is provided and the quadratical convergence is proved. Moreover, numerical experiments are given in the last section to illustrate our results.