Nonstationary Extrapolated Modulus Algorithms for the solution of the Linear Complementarity Problem

The Linear Complementarity Problem (LCP) has many applications as, e.g., in the solution of Linear and Convex Quadratic Programming, in Free Boundary Value problems of Fluid Mechanics, etc. In the present work we assume that the matrix coefficient M∈Rn,nCCCCcCof the LCP is symmetric positive definite and we introduce the (optimal) nonstationary extrapolation to improve the convergence rates of the well-known Modulus Algorithm and Block Modulus Algorithm for its solution. Two illustrative numerical examples show that the (Optimal) Nonstationary Extrapolated Block Modulus Algorithm is far better than all the previous similar Algorithms.