A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex
<|reference_start|>A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex: 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.<|reference_end|>
@article{eisenmann2024a,
    title={A Newton method for solving locally definite multiparameter eigenvalue
  problems by multiindex},
    author={Henrik Eisenmann},
    journal={arXiv preprint arXiv:2404.04194},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.04194},
    primaryClass={math.NA cs.NA}
}