Numerical solution to a linear equation with tensor product structure

Hung-Yuan Fan, Liping Zhang, Eric King wah Chu, Yimin Wei

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider the numerical solution of a c-stable linear equation in the tensor product space ℝn1x...xnd, arising from a discretized elliptic partial differential equation in ℝd. Utilizing the stability, we produce an equivalent d-stable generalized Stein-like equation, which can be solved iteratively. For large-scale problems defined by sparse and structured matrices, the methods can be modified for further efficiency, producing algorithms of O(Σini)+O(ns) computational complexity, under appropriate assumptions (with ns being the flop count for solving a linear system associated with Ai-γIni). Illustrative numerical examples will be presented.

Original languageEnglish
Article numbere2106
JournalNumerical Linear Algebra with Applications
Volume24
Issue number6
DOIs
Publication statusPublished - 2017 Dec 1

Keywords

  • Cayley transform
  • Kronecker product
  • Stein equation
  • Sylvester equation
  • elliptic partial differential equation
  • large-scale problem
  • linear equation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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