Approximate Cayley transform methods for inverse eigenvalue problems and convergence analysis

Based on an approximation to Cayley transform, we propose an approximate Cayley transform method and its inexact version for solving inverse eigenvalue problems, which has the advantage over other known methods in the sense that it avoids solving systems in obtaining the approximate eigenvectors. Under the nonsingular condition used in D. Sun and J. Sun [29], we show that the proposed methods converge at least superlinearly. Moreover, numerical experiments are given which illustrate that, comparing with the Cayley transform methods, our methods need much less inner iterations and CPU time.