Solving Singular Generalized Eigenvalue Problems by a Rank-Completing Perturbation

A Smallest Singular Value Method for Solving Inverse Eigenvalue Problems

Utilizing the properties of the smallest singular value of a matrix, we propose a new, efficient and reliable algorithm for solving nonsymmetric matrix inverse eigenvalue problems, and compare it with a known method. We also present numerical experiments which illustrate our results.

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

Erratum: Perturbation of Partitioned Hermitian Definite Generalized Eigenvalue Problems

The main purpose of this erratum is to correct mistakes in the proof of Theorem 2.4 of [R.-C. Li et al., SIAM J. Matrix Anal. Appl., 32 (2011), pp. 642–663] and in the inequalities (2.23), (2.24), and (2.25) on p. 653 of the same paper.

Perturbation of Partitioned Hermitian Definite Generalized Eigenvalue Problems

This paper is concerned with the Hermitian definite generalized eigenvalue problem A− λB for block diagonal matrices A 1⁄4 diagðA11; A22Þ and B 1⁄4 diagðB11; B22Þ. Both A and B are Hermitian, and B is positive definite. Bounds on how its eigenvalues vary when A and B are perturbed by Hermitian matrices are established. These bounds are generally of linear order with respect to the perturbations...

Solving nonlinear eigenvalue problems