Nonlinear eigenvalue problems arise in a variety of science and engineering applications,
and in the past ten years there have been numerous breakthroughs in the development of …

We survey the quadratic eigenvalue problem, treating its many applications, its
mathematical properties, and a variety of numerical solution techniques. Emphasis is given …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

We discuss the state of the art in numerical solution methods for large scale polynomial or
rational eigenvalue problems. We present the currently available solution methods such as …

For the nonlinear eigenvalue problem T (λ) x= 0 we propose an iterative projection method
for computing a few eigenvalues close to a given parameter. The current search space is …

A new rational Krylov method for the efficient solution of nonlinear eigenvalue problems,
A(λ)x=0, is proposed. This iterative method, called fully rational Krylov method for nonlinear …

The Arnoldi method for standard eigenvalue problems possesses several attractive
properties making it robust, reliable and efficient for many problems. The first result of this …

This paper discusses a projection method for nonlinear eigenvalue problems. The subspace
of approximants is constructed by a Jacobi–Davidson-type approach, and the arising …

The linear FEAST algorithm is a method for solving linear eigenvalue problems. It uses
complex contour integration to calculate the eigenvectors associated with eigenvalues that …

The Arnoldi method is currently a very popular algorithm to solve large-scale eigenvalue
problems. The main goal of this paper is to generalize the Arnoldi method to the …