A generic multiresolution preconditioner for sparse symmetric systems

We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain. In constrast, based on the recently proposed Multiresolutio...

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Bibliographic Details
Main Authors Mudrakarta, Pramod Kaushik, Kondor, Risi
Format Journal Article
LanguageEnglish
Published 07.07.2017
Subjects
Mathematics - Numerical Analysis
Online AccessGet full text
DOI10.48550/arxiv.1707.02054

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Summary:We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain. In constrast, based on the recently proposed Multiresolution Matrix Factorization (MMF) algorithm, we construct a preconditioner that discovers a custom wavelet basis adapted to the given linear system without making any geometric assumptions. Some advantages of the new approach are fast preconditioner-vector products, invariance to the ordering of the rows/columns, and the ability to handle systems of any size. Numerical experiments on finite difference discretizations of model PDEs and off-the-shelf matrices illustrate the effectiveness of the MMF preconditioner.
DOI:10.48550/arxiv.1707.02054