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

Generalized rational Krylov decompositions are matrix relations which, under certain
conditions, are associated with rational Krylov spaces. We study the algebraic properties of …

We present a method for solving nonlinear eigenvalue problems (NEPs) using rational
approximation. The method uses the Antoulas–Anderson algorithm (AAA) of Nakatsukasa …

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 …

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 …

Lamb waves are elastodynamic guided waves in plates and are used for non-destructive
evaluation, sensors, and material characterization. These applications rely on the …

Rosenbrock's theorem on polynomial system matrices is a classical result in linear systems
theory that relates the Smith-McMillan form of a rational matrix G with the Smith form of an …

For several decades, the coupled boundary element and finite element (BE–FE) approach
has been recognized as a potential tool for modeling sound–structure interaction problems …

This paper defines for the first time strong linearizations of arbitrary rational matrices, studies
in depth properties and characterizations of such linear matrix pencils, and develops …