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.

in this paper, we represent an inexact inverse subspace iteration method for com- puting 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.

We study the local convergence of several inexact numerical algorithms closely related to Newton’s method for the solution of a simple eigenpair of the general nonlinear eigenvalue problem T (λ)v = 0. We investigate inverse iteration, Rayleigh quotient iteration, residual inverse iteration, and the single-vector Jacobi-Davidson method, analyzing the impact of the tolerances chosen for the appro...

Convergence results are provided for inexact two-sided inverse and Rayleigh quotient iteration, which extend the previously established results to the generalized eigenproblem, and inexact solves with a decreasing solve tolerance. Moreover, the simultaneous solution of the forward and adjoint problem arising in two-sided methods is considered and the successful tuning strategy for preconditione...

In this paper we analyse inexact inverse iteration for the real symmetric eigenvalue problem Av = λv. Our analysis is designed to apply to the case when A is large and sparse and where iterative methods are used to solve the shifted linear systems (A − σI)y = x which arise. We rst present a general convergence theory that is independent of the nature of the inexact solver used. Next we consider...

In this paper, we propose an inexact inverse iteration method for the computation of the eigenvalue with the smallest modulus and its associated eigenvector for a large sparse matrix. The linear systems of the traditional inverse iteration are solved with accuracy that depends on the eigenvalue with the second smallest modulus and iteration numbers. We prove that this approach preserves the lin...

We propose and study the iteration-complexity of an inexact version of the Spingarn’s partial inverse method. Its complexity analysis is performed by viewing it in the framework of the hybrid proximal extragradient (HPE) method, for which pointwise and ergodic iteration-complexity has been established recently by Monteiro and Svaiter. As applications, we propose and analyze the iteration-comple...

Inexact Newton regularization methods have been proposed by Hanke and Rieder for solving nonlinear ill-posed inverse problems. Every such a method consists of two components: an outer Newton iteration and an inner scheme providing increments by regularizing local linearized equations. The method is terminated by a discrepancy principle. In this paper we consider the inexact Newton regularizatio...