Analysis of first order systems for the solution of Laplace's equation

2014/04/13 by Vance Faber, Faber, Vance
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #math.CO

paper · pdf · doi:10.48550/arxiv.1404.3420

10 pages

arxiv created 2014/04/13 · openalex publication_date 2014/04/13 · arxiv updated 2014/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Kelner, Orecchia, Sidford, and Zhu have given a randomized iterative method for approximating the solution to the discrete Laplace equation that has expected running time nearly linear in the size of the problem. The goal of this note is to explain this algorithm in the language of difference operators on graphs.

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