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Regularized solution of LCP problems with application to rigid body dynamics

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Abstract

For Linear Complementarity Problems (LCP) with a positive semidefinite matrix M, iterative solvers can be derived by a process of regularization. In [3] the initial LCP is replaced by a sequence of positive definite ones, with the matrices M + αI. Here we analyse a generalization of this method where the identity I is replaced by a positive definite diagonal matrix D. We prove that the sequence of approximations so defined converges to the minimal D-norm solution of the initial LCP. This extension opens the possibility for interesting applications in the field of rigid multibody dynamics.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Ovidius University, Blvd. Mamaia 124, Constanta, 900527, Romania

    Constantin Popa

  2. Gheorghe Mihoc - Caius Iacob Institute of Statistical Mathematics and Applied Mathematics of the Romanian Academy, Calea 13 Septembrie, Nr. 13, Bucharest, 050711, Romania

    Constantin Popa

  3. Department of Computer Science 10 (System Simulation), Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Tobias Preclik & Ulrich Rüde

Authors
  1. Constantin Popa
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  2. Tobias Preclik
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  3. Ulrich Rüde
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Correspondence to Constantin Popa.

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Popa, C., Preclik, T. & Rüde, U. Regularized solution of LCP problems with application to rigid body dynamics. Numer Algor 69, 145–156 (2015). https://doi.org/10.1007/s11075-014-9886-0

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  • DOI: https://doi.org/10.1007/s11075-014-9886-0

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