### 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 language | English |
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Pages (from-to) | 291-301 |

Number of pages | 11 |

Journal | Applied Numerical Mathematics |

Volume | 21 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jul 1996 |

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### Keywords

- block structure
- linear systems
- invariant manifolds

### Cite this

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*Applied Numerical Mathematics*, vol. 21, no. 3, pp. 291-301. https://doi.org/10.1016/0168-9274(96)00013-X

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - A structured matrix problem in dynamical systems

AU - Ramage, Alison

PY - 1996/7/1

Y1 - 1996/7/1

N2 - 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.

AB - 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.

KW - block structure

KW - linear systems

KW - invariant manifolds

UR - http://www.scopus.com/inward/record.url?scp=0030189095&partnerID=8YFLogxK

U2 - 10.1016/0168-9274(96)00013-X

DO - 10.1016/0168-9274(96)00013-X

M3 - Article

AN - SCOPUS:0030189095

VL - 21

SP - 291

EP - 301

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

IS - 3

ER -