2 results for Askes, Harm

  • Tyings in linear systems of equations modelled with positive and negative penalty functions

    Askes, Harm; Piercy, Stewart; Ilanko, Sinniah (2008)

    Journal article
    University of Waikato

    In this short note, we focus on tyings (constraints that relate multiple degrees of freedom) modelled by means of penalty functions. In contrast to what is commonly thought, it is possible to obtain convergent results when negative penalty parameters are taken. A mathematical proof and an illustrating example are provided. In particular, we have proven that the results obtained with positive and negative penalty parameters enclose the exact solution from opposite sides. To this end, we have investigated a pseudo-force that is defined as the derivative of the constraint with respect to the inverse penalty parameter.

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  • The use of negative penalty functions in linear systems of equations

    Askes, Harm; Ilanko, Sinniah (2006)

    Journal article
    University of Waikato

    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.

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