A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex
H Eisenmann - arXiv preprint arXiv:2404.04194, 2024 - arxiv.org
arXiv preprint arXiv:2404.04194, 2024•arxiv.org
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 …
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 …
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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