A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex

Henrik Eisenmann

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arXiv · 2404.04194

A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex

Henrik Eisenmann

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Abstract

We present a new approach to compute eigenvalues and eigenvectors of locally definite multiparameter eigenvalue problems by its signed multiindex. 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.

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Henrik Eisenmann. 2024-04-05. A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex. https://arxiv.org/abs/2404.04194

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