13 research outputs found
IGAOR and multisplitting IGAOR methods for linear complementarity problems
AbstractIn this paper, we propose an interval version of the generalized accelerated overrelaxation methods, which we refer to as IGAOR, for solving the linear complementarity problems, LCP (M, q), and develop a class of multisplitting IGAOR methods which can be easily implemented in parallel. In addition, in regards to the H-matrix with positive diagonal elements, we prove the convergence of these algorithms and illustrate their efficiency through our numerical results
New Relaxation Modulus Based Iterative Method for Large and Sparse Implicit Complementarity Problem
This article presents a class of new relaxation modulus-based iterative
methods to process the large and sparse implicit complementarity problem (ICP).
Using two positive diagonal matrices, we formulate a fixed-point equation and
prove that it is equivalent to ICP. Also, we provide sufficient convergence
conditions for the proposed methods when the system matrix is a -matrix or
an -matrix.
Keyword: Implicit complementarity problem, -matrix, -matrix, matrix
splitting, convergenceComment: arXiv admin note: substantial text overlap with arXiv:2303.1251
Asynchronous iterations with flexible communication: contracting operators
AbstractThe concept of flexible communication permits one to model efficient asynchronous iterations on parallel computers. This concept is particularly useful in two practical situations. Firstly, when communications are requested while a processor has completed the current update only partly, and secondly, in the context of inner/outer iterations, when processors are also allowed to make use of intermediate results obtained during the inner iteration in other processors.In the general case of nonlinear or linear fixed point problems, we give a global convergence results for asynchronous iterations with flexible communication whereby the iteration operators satisfy certain contraction hypotheses. In this manner we extend to a contraction context previous results obtained for monotone operators with respect to a partial ordering
On preconditioned SSOR methods for the linear complementarity problem
In this paper, we consider the preconditioned iterative methods for solving the linear complementarity problem associated with an M-matrix. Two preconditioned SSOR methods for solving the linear complementarity problem are proposed. The convergence of the proposed methods are analyzed, and the comparison results are derived. The comparison results show that the proposed preconditioned SSOR methods accelerate the convergent rate of the SSOR method. Numerical experiments verify the theory results
A BLOCK-PARALLEL CONJUGATE GRADIENT METHOD FOR SEPARABLE QUADRATIC PROGRAMMING PROBLEMS1
Abstract For a large-scale quadratic programming problem with separable objective function, a variant of the conjugate gradient method can effectively be applied to the dual problem. In this paper, we consider a block-parallel modification of the conjugate gradient method, which is suitable for implementation on a parallel computer. More precisely, the method proceeds in a block Jacobi manner and executes the conjugate gradient iteration to solve quadratic programming subproblems associated with respective blocks. We implement the method on a Connection Machine Model CM-5 in the Single-Program Multiple-Data model of computation. We report some numerical results, which show that the proposed method is effective particularly for problems with some block structure
On general fixed point method based on matrix splitting for solving linear complementarity problem
In this article, we introduce a modified fixed point method to process the large and sparse linear complementarity problem (LCP) and formulate an equivalent fixed point equation for the LCP and show the equivalence. Also, we provide convergence conditions when the system matrix is a -matrix and two sufficient convergence conditions when the system matrix is an -matrix. To show the efficiency of our proposed method, we illustrate two numerical examples for different parameters