Regularized solution of LCP problems with application to rigid body dynamics
For Linear Complementarity Problems (LCP) with a positive semidefinite matrix M, iterative solvers can be derived by a process of regularization. In  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.
KeywordsLinear complementarity problem Splitting method Regularization Weighted minimal norm solutions Rigid body dynamics
Mathematics Subject Classifications (2010)65F10 65J20 65F20
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