2024/12/29 by Patrick Erik Bradley, Bradley, Patrick Erik · 2 citations
Mathematics · Computer Science · #advanced mathematical theories #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2412.20591
The error estimation for eigenvalues and eigenvectors of a small positive symmetric perturbation on the spectrum of a graph Laplacian is related to Gauß hypergeometric functions. Based on this, a heuristic polynomial-time algorithm for finding an optimal locally ultrametric approximation of a graph-distance power Laplacian matrix via the Vietoris-Rips graph based on the graph distance function is proposed. In the end, the error in the solution to the graph Laplacian heat equation given by extension to a locally p-adic equation is estimated.