A quadratically convergent algorithm for inverse generalized eigenvalue problems

摘要

In 2018, for inverse generalized symmetric eigenvalue problems, a new quadratically convergent algorithm was discovered from simple matrix equations. Although this algorithm has some nice features compared with the standard Newton's method, it cannot be applied to multiple eigenvalues. In this paper, we propose a modified algorithm adapted to an arbitrary set of prescribed eigenvalues. Moreover, we prove its quadratic convergence in a neighborhood of the solutions that satisfy a mild condition. (C) 2019 Elsevier B.V. All rights reserved.