Refining estimates of invariant and deflating subspaces for large and sparse matrices and pencils

Hung-Yuan Fan, Peter Chang Yi Weng, Eric King wah Chu

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider the refinement of estimates of invariant (or deflating) subspaces for a large and sparse real matrix (or pencil) in ℝn×n, through some (generalized) nonsymmetric algebraic Riccati equations or their associated (generalized) Sylvester equations via Newton's method. The crux of the method is the inversion of some well-conditioned unstructured matrices via the efficient and stable inversion of the associated structured but near-singular matrices.All computations have complexity proportional to n, under appropriate assumptions, as illustrated by several numerical examples.

Original languageEnglish
Pages (from-to)147-169
Number of pages23
JournalBIT Numerical Mathematics
Volume54
Issue number1
DOIs
Publication statusPublished - 2014 Jan 1

Keywords

  • Deflating subspace
  • Invariant subspace
  • Large-scale problem
  • Newton's method
  • Nonsymmetric algebraic Riccati equation
  • Sparse matrix
  • Sylvester equation

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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