We present a refined Arnoldi-type method for extracting partial eigenpairs of large matrices.
The approximate eigenvalues are the Ritz values of (A− τ I)− 1 with respect to a shifted …

This paper presents an invert-free Arnoldi method for extracting a few interior eigenpairs of
large sparse matrices. It is derived by implicitly applying the Arnoldi process with the shifted …

Arnoldi method approximates exterior eigenvalues of a large sparse matrix, but may fail to
approximate corresponding eigenvectors. The refined Arnoldi method approximates an …

Arnoldi's method has been popular for computing the small number of selected eigenvalues
and the associated eigenvectors of large unsymmetric matrices. However, the approximate …

The shift-and-invert Arnoldi method has been popularly used for computing a number of
eigenvalues close to a given shift and/or the associated eigenvectors of a large unsymmetric …

The Arnoldi method is a commonly used technique for finding a few eigenpairs of large,
sparse and nonsymmetric matrices. Recently, a new variant of Arnoldi method (NVRA) was …

Many methods for the computation of selected eigenpairs of generalized eigenproblems for
matrix pairs use a shift-and-invert technique. When applied to large-scale problems, this …

This paper describes a method for computing the dominant/right-most eigenvalues of large
matrices. The method consists of refining the approximate eigenelements of a large matrix …

When combined with Krylov projection methods, polynomial filtering can provide a powerful
method for extracting extreme or interior eigenvalues of large sparse matrices. This general …

Based on the implicitly restarted Arnoldi method for eigenpairs of large matrix, a new method
is presented for the computation of a few eigenpairs and their derivatives of large matrix …