A structured matrix problem in dynamical systems

Research output: Contribution to journalArticle

Abstract

This paper considers the iterative solution of a class of nonsymmetric linear systems where the coefficient matrices have a very specific block structure. These arise in the context of dynamical systems when computing a smooth invariant manifold for the forced van der Pol oscillator. A pseudo-spectral approximation method is described to explain the origin of the matrix structure and efficient solution of the linear equations is discussed. The convergence behaviour of three widely used nonsymmetric iterative methods is illustrated using numerical experiments.

Original languageEnglish
Pages (from-to)291-301
Number of pages11
JournalApplied Numerical Mathematics
Volume21
Issue number3
DOIs
Publication statusPublished - 1 Jul 1996

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Structured Matrices
Dynamical systems
Dynamical system
Nonsymmetric Linear Systems
Spectral Approximation
Van Der Pol Oscillator
Block Structure
Pseudospectral Method
Smooth Manifold
Invariant Manifolds
Iterative Solution
Iterative methods
Linear equations
Efficient Solution
Approximation Methods
Linear systems
Linear equation
Numerical Experiment
Iteration
Computing

Keywords

  • block structure
  • linear systems
  • invariant manifolds

Cite this

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A structured matrix problem in dynamical systems. / Ramage, Alison.

In: Applied Numerical Mathematics, Vol. 21, No. 3, 01.07.1996, p. 291-301.

Research output: Contribution to journalArticle

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