Tensor properties of multilevel Toeplitz and related matrices

Vadim Olshevsky, Ivan Oseledets, Eugene Tyrtyshnikov

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)

Abstract

A general proposal is presented for fast algorithms for multilevel structured matrices. It is based on investigation of their tensor properties and develops the idea recently introduced by Kamm and Nagy in the block Toeplitz case. We show that tensor properties of multilevel Toeplitz matrices are related to separation of variables in the corresponding symbol, present analytical tools to study the latter, expose truncation algorithms preserving the structure, and report on some numerical results confirming advantages of the proposal.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalLinear Algebra and Its Applications
Volume412
Issue number1
DOIs
Publication statusPublished - 1 Jan 2006
Externally publishedYes

Keywords

  • Asymptotically smooth functions
  • Kronecker product
  • Low-rank matrices
  • Multilevel matrices
  • Separation of variables
  • Toeplitz matrices

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