Approximating the inverse of a diagonally dominant matrix with positive elements

2019/02/02 by Ting Yan, Yan, Ting
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1902.00668

openalex publication_date 2019/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

For an n× n diagonally dominant matrix T=(t_i,j)_{n× n} with positive elements satisfying certain bounding conditions, we propose to use a diagonal matrix S=(s_i,j)_{n× n} to approximate the inverse of T, where s_i,j=δ_i,j/t_i,i and δ_i,j is the Kronecker delta function. We derive an explicitly upper bound on the approximation error, which is in the magnitude of O(n^-2). It shows that S is a very good approximation to T^-1.

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