Numerical solution to a linear equation with tensor product structure

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

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4 Citations (Scopus)

Abstract

We consider the numerical solution of a c-stable linear equation in the tensor product space Rn1×...×nd, 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(∑ini)+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
Number of pages18
JournalNumerical Linear Algebra with Applications
Volume24
Issue number6
DOIs
Publication statusPublished - Dec 2017

Keywords

  • Cayley transform
  • Elliptic partial differential equation
  • Kronecker product
  • Large-scale problem
  • Linear equation
  • Stein equation
  • Sylvester equation

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