On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations

Fatemeh Panjeh Ali Beik, Farid Saberi Movahed, Salman Ahmadi-Asl

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)

Abstract

This paper deals with studying some of well-known iterative methods in their tensor forms to solve a Sylvester tensor equation. More precisely, the tensor form of the Arnoldi process and full orthogonalization method are derived by using a product between two tensors. Then tensor forms of the conjugate gradient and nested conjugate gradient algorithms are also presented. Rough estimation of the required number of operations for the tensor form of the Arnoldi process is obtained, which reveals the advantage of handling the algorithms based on tensor format over their classical forms in general. Some numerical experiments are examined, which confirm the feasibility and applicability of the proposed algorithms in practice.

Original languageEnglish
Pages (from-to)444-466
Number of pages23
JournalNumerical Linear Algebra with Applications
Volume23
Issue number3
DOIs
Publication statusPublished - 1 May 2016
Externally publishedYes

Keywords

  • Arnoldi process
  • Krylov subspace method
  • Nested iterations
  • Sylvester tensor equation

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