On sparse representations of linear operators and the approximation of matrix products

Mohamed Ali Belabbas, Patrick J. Wolfe

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

Abstract

Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under consideration is sparse is used to decrease the number of necessary measurements while controlling the approximation error. In this paper, we instead focus on applications in numerical analysis, by way of sparse representations of linear operators with the objective of minimizing the number of operations needed to perform basic operations (here, multiplication) on these operators. We represent a linear operator by a sum of rank-one operators, and show how a sparse representation that guarantees a low approximation error for the product can be obtained from analyzing an induced quadratic form. This construction in turn yields new algorithms for computing approximate matrix products.

Original languageEnglish (US)
Title of host publicationCISS 2008, The 42nd Annual Conference on Information Sciences and Systems
Pages258-263
Number of pages6
DOIs
StatePublished - 2008
Externally publishedYes
EventCISS 2008, 42nd Annual Conference on Information Sciences and Systems - Princeton, NJ, United States
Duration: Mar 19 2008Mar 21 2008

Publication series

NameCISS 2008, The 42nd Annual Conference on Information Sciences and Systems

Other

OtherCISS 2008, 42nd Annual Conference on Information Sciences and Systems
CountryUnited States
CityPrinceton, NJ
Period3/19/083/21/08

ASJC Scopus subject areas

  • Computer Science Applications
  • Information Systems
  • Control and Systems Engineering

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