Sketching for Motzkin's Iterative Method for Linear Systems

Elizaveta Rebrova, Deanna Needell

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Projection-based iterative methods for solving large over-determined linear systems are well-known for their simplicity and computational efficiency. It is also known that the correct choice of a sketching procedure (i.e., preprocessing steps that reduce the dimension of each iteration) can improve the performance of iterative methods in multiple ways, such as, to speed up the convergence of the method by fighting inner correlations of the system, or to reduce the variance incurred by the presence of noise. In the current work, we show that sketching can also help us to get better theoretical guarantees for the projection-based methods. Specifically, we use good properties of Gaussian sketching to prove an accelerated convergence rate of the sketched relaxation (also known as Motzkin's) method. The new estimates hold for linear systems of arbitrary structure. We also provide numerical experiments in support of our theoretical analysis of the sketched relaxation method.

Original languageEnglish (US)
Title of host publicationConference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages271-275
Number of pages5
ISBN (Electronic)9781728143002
DOIs
StatePublished - Nov 2019
Externally publishedYes
Event53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019 - Pacific Grove, United States
Duration: Nov 3 2019Nov 6 2019

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2019-November
ISSN (Print)1058-6393

Conference

Conference53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
Country/TerritoryUnited States
CityPacific Grove
Period11/3/1911/6/19

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Networks and Communications

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