The computation of Jordan blocks in parameter-dependent matrices

Richard O Akinola; Melina A Freitag; Alistair Spence

doi:10.1093/imanum/drt028

The computation of Jordan blocks in parameter-dependent matrices

Richard O Akinola, Melina A Freitag, Alistair Spence

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Abstract

This paper extends the implicit determinant method introduced by Spence & Poulton (2005, J. Comput. Phys., 204, 65–81) to obtain a numerical technique for the calculation of a two-dimensional Jordan block in a parameter-dependent matrix. An important feature of this technique is that the theory is straightforward to understand and an efficient numerical implementation is suggested naturally by the theory. Three interesting physical problems are presented, arising from the panel flutter problem in aerodynamics, the stability of electrical power systems and a problem in quantum mechanics.

Original language	English
Pages (from-to)	955-976
Number of pages	22
Journal	IMA Journal of Numerical Analysis
Volume	34
Issue number	3
Early online date	24 Sept 2013
DOIs	https://doi.org/10.1093/imanum/drt028
Publication status	Published - Jul 2014

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This is a pre-copyedited, author-produced PDF of an article accepted for publication in the Journal of Numerical Anaysis following peer review. The definitive publisher-authenticated version Freitag, MA 2013, 'The computation of Jordan blocks in parameter-dependent matrices' IMA Journal of Numerical Analysis is available online at: http://imajna.oxfordjournals.org/content/early/2013/09/24/imanum.drt028
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AB - This paper extends the implicit determinant method introduced by Spence & Poulton (2005, J. Comput. Phys., 204, 65–81) to obtain a numerical technique for the calculation of a two-dimensional Jordan block in a parameter-dependent matrix. An important feature of this technique is that the theory is straightforward to understand and an efficient numerical implementation is suggested naturally by the theory. Three interesting physical problems are presented, arising from the panel flutter problem in aerodynamics, the stability of electrical power systems and a problem in quantum mechanics.

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The computation of Jordan blocks in parameter-dependent matrices

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