Entrywise Approximate Solutions for SDDM Systems in Almost-Linear Time

Fuente: arXiv
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Autori principali: Farfan, Angelo, Ghadiri, Mehrdad, Yang, Junzhao
Natura: Preprint
Pubblicazione: 2025
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author Farfan, Angelo
Ghadiri, Mehrdad
Yang, Junzhao
author_facet Farfan, Angelo
Ghadiri, Mehrdad
Yang, Junzhao
contents We present an algorithm that given any invertible symmetric diagonally dominant M-matrix (SDDM), i.e., a principal submatrix of a graph Laplacian, $\boldsymbol{\mathit{L}}$ and a nonnegative vector $\boldsymbol{\mathit{b}}$, computes an entrywise approximation to the solution of $\boldsymbol{\mathit{L}} \boldsymbol{\mathit{x}} = \boldsymbol{\mathit{b}}$ in $\tilde{O}(m n^{o(1)})$ time with high probability, where $m$ is the number of nonzero entries and $n$ is the dimension of the system.
format Preprint
id arxiv_https___arxiv_org_abs_2511_16570
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Entrywise Approximate Solutions for SDDM Systems in Almost-Linear Time
Farfan, Angelo
Ghadiri, Mehrdad
Yang, Junzhao
Data Structures and Algorithms
Numerical Analysis
65F10
F.2.1; G.1.3
We present an algorithm that given any invertible symmetric diagonally dominant M-matrix (SDDM), i.e., a principal submatrix of a graph Laplacian, $\boldsymbol{\mathit{L}}$ and a nonnegative vector $\boldsymbol{\mathit{b}}$, computes an entrywise approximation to the solution of $\boldsymbol{\mathit{L}} \boldsymbol{\mathit{x}} = \boldsymbol{\mathit{b}}$ in $\tilde{O}(m n^{o(1)})$ time with high probability, where $m$ is the number of nonzero entries and $n$ is the dimension of the system.
title Entrywise Approximate Solutions for SDDM Systems in Almost-Linear Time
topic Data Structures and Algorithms
Numerical Analysis
65F10
F.2.1; G.1.3
url https://arxiv.org/abs/2511.16570