Abstract
This paper aims to show that the existing preconditioned symmetric successive over-relaxation (SSOR) approach to solving the linear complementarity problem (LCP) is not valid. To overcome the flaws, we propose an efficient preconditioner called the monomial preconditioner. The convergence behavior of the proposed model is also established. Meanwhile, the efficiency of the new method is verified by numerical experiments.
Highlights
The Linear Complementarity Problem (LCP) with an n × n matrix A and an n-dimensional vector q is to find two nonnegative vectors z, w ∈ Rn such that:w = Az + q ≥ 0, zT w = 0. (1)This problem has many application in science and engineering problems, e.g., mathematical programming, economics, game theory, contact problems, structural mechanics, journal bearings, circuit simulation, etc
Yuan and Song [35] developed the convergence of the so-called Modified Accelerated Overrelaxation (MAOR) and Modified Successive Overrelaxation (MSOR) methods for the solution of the linear complementarity problem (LCP) when the matrix A belongs to the class of 2-cyclic matrices
THE EXISTING PRECONDITIONED successive over-relaxation (SSOR) METHOD FOR LCP The improvement of genuine preconditioning strategies in iterative modeling is the key for the fruitful utilization of computations for solving of numerous scientific problems
Summary
The Linear Complementarity Problem (LCP) with an n × n matrix A and an n-dimensional vector q is to find two nonnegative vectors z, w ∈ Rn such that:. When the matrix A is large and sparse, the stationary iterative methods are often considered for the solution of LCP (1) One type of these methods is the modulus iterative algorithms that was pioneered by van Bokhoven [8]. (see, e.g., [19]–[27] and the references therein) Another class of the stationary iterative methods to solve LCPs is called the projected iterative methods. Yuan and Song [35] developed the convergence of the so-called Modified Accelerated Overrelaxation (MAOR) and Modified Successive Overrelaxation (MSOR) methods for the solution of the LCP when the matrix A belongs to the class of 2-cyclic matrices.
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