A Newton Method for Solving Locally Definite Multiparameter Eigenvalue Problems by Multi-index

SIAM Journal on Matrix Analysis and Applications, vol. 46, pp. 906–933

Abstract

Abstract. We present a new approach to compute eigenvalues and eigenvectors of locally definite multiparameter eigenvalue problems by their signed multi-index. The method has the interpretation of a semismooth Newton method applied to certain functions that have a unique zero. We can therefore show local quadratic convergence, and for certain extreme eigenvalues even global linear convergence of the method. Local definiteness is a weaker condition than right and left definiteness, which is often considered for multiparameter eigenvalue problems. These conditions are naturally satisfied for multiparameter Sturm–Liouville problems that arise when separation of variables can be applied to multidimensional boundary eigenvalue problems.

Authors 1

1. Henrik Eisenmann corresponding Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, 52062 Aachen, Germany