Improving projected successive overrelaxation method for linear complementarity problems Original Research Article

Projected Successive OverRelaxation (PSOR), an important method for solving Linear Complementarity Problems (LCPs), can be improved considerably if one takes into account the underlying physical properties of the problem involved. We show this for LCPs arising in the context of Moving Boundary Problems and in the case of the American Options Valuation Problem. For such problems, a time stepping procedure is necessary in which one has to solve a sequence of discrete LCPs, one per each time step. In this case, a moving (unknown) boundary separates two domains over which different solution properties hold. Taking advantage of this separation leads to an implementation of PSOR for problems of smaller dimension. This, in turn, leads to a new iterative scheme, which is up to 50% faster compared to plain PSOR.