2020/08/07 by Henrik Eisenmann, Yuji Nakatsukasa, Eisenmann, Henrik +1 · 1 citation
Chemistry · Computer Science · Materials Science · #Advanced NMR Techniques and Applications #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #X-ray Diffraction in Crystallography
paper · pdf · doi:10.48550/arxiv.2008.03385
openalex publication_date 2020/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter eigenvalue problem. The method is applicable for right definite problems, possibly after performing an affine transformation. This includes a class of Helmholtz equations when separation of variables is applied. We provide a convergence proof for extremal eigenvalues and empirical evidence along with a local convergence proof for other eigenvalues.