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 …

This book is designed to be used by mathematicians, engineers, and computer scientists as
a graduate-level introduction to numerical analysis and its methods. Readers are expected …

We present two approximation methods for computing eigenfrequencies and eigenmodes of
large-scale nonlinear eigenvalue problems resulting from boundary element method (BEM) …

We develop a new algorithm for the computation of all the eigenvalues and optionally the
right and left eigenvectors of dense quadratic matrix polynomials. It incorporates scaling of …

The concept of linearization is fundamental for theory, applications, and spectral
computations related to matrix polynomials. However, recent research on several important …

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 …

A standard way of dealing with a matrix polynomial P(λ) is to convert it into an equivalent
matrix pencil—a process known as linearization. For any regular matrix polynomial, a new …

We introduce a new family of strong linearizations of matrix polynomials—which we call
“block Kronecker pencils”—and perform a backward stability analysis of complete …

We propose a new uniform framework of compact rational Krylov (CORK) methods for
solving large-scale nonlinear eigenvalue problems A(λ)x=0. For many years, linearizations …

This work is concerned with numerical methods for matrix eigenvalue problems that are
nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for …