dc.contributor.author Askes, Harm dc.contributor.author Ilanko, Sinniah dc.date.accessioned 2014-01-15T22:54:38Z dc.date.available 2014-01-15T22:54:38Z dc.date.copyright 2006-10-08 dc.date.issued 2006 dc.identifier.citation Askes, H., & Ilanko, S. (2006). The use of negative penalty functions in linear systems of equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 462(2074), 2965-2975. en_NZ dc.identifier.uri https://hdl.handle.net/10289/8398 dc.description.abstract Contrary to what is commonly thought, it is possible to obtain convergent results with negative (rather than positive) penalty functions. This has been shown and proven on various occasions for vibration analysis, but in this contribution it will also be shown and proven for systems of linear equations subjected to one or more constraints. As a key ingredient in the developed arguments, a pseudo-force is identified as the derivative of the constrained degree of freedom with respect to the inverse of the penalty parameter. Since this pseudo-force can be proven to be constant for large absolute values of the penalty parameter, it follows that the exact solution is bounded by the results obtained with negative and positive penalty parameters. The mathematical proofs are presented and two examples are shown to illustrate the principles. en_NZ dc.language.iso en en_NZ dc.publisher Royal Society en_NZ dc.relation.ispartof Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences dc.relation.uri http://rspa.royalsocietypublishing.org/content/462/2074/2965.full en_NZ dc.subject constraint en_NZ dc.subject penalty function en_NZ dc.subject asymptotic modelling en_NZ dc.title The use of negative penalty functions in linear systems of equations en_NZ dc.type Journal Article en_NZ dc.identifier.doi 10.1098/rspa.2006.1716 en_NZ dc.relation.isPartOf Royal Society of London. Proceedings. Mathematical, Physical and Engineering Sciences en_NZ pubs.begin-page 2965 en_NZ pubs.elements-id 34156 pubs.end-page 2975 en_NZ pubs.issue 2074 en_NZ pubs.volume 462 en_NZ
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