Fiber product homotopy method for multiparameter eigenvalue problems
نویسندگان
چکیده
We develop a new homotopy method for solving multiparameter eigenvalue problems (MEPs) called the fiber product method. For k-parameter problem with matrices of sizes $$n_1,\ldots ,n_k = O(n)$$ , requires deformation O(1) linear equations, while existing methods MEPs require O(n) nonlinear equations. show that theoretically finds all eigenpairs an MEP probability one. It is especially well-suited class we call dimension-deficient singular are generic respect to intrinsic dimension, as provably convergent one such well, fact borne out by numerical experiments. More generally, our experiments indicate significantly outperforms standard Delta in terms accuracy, consistent backward errors on order $$10^{-16}$$ without any use extended precision. In speed, it previous homotopy-based and larger problems, also highly parallelizable. solve method, although mathematically equivalent MEP, typically much better conditioned problem.
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ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2021
ISSN: ['0945-3245', '0029-599X']
DOI: https://doi.org/10.1007/s00211-021-01215-6