On convergence of two-stage splitting methods for linear complementarity problems

Convergence analysis of modulus-based matrix splitting iterative methods for implicit complementarity problems

In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra Appl. 23:629-641, 2016). New convergence conditions are presented when the system matrix is a positive-definite matrix and an [Formula: see text]-matrix, respecti...

Improved infeasible-interior-point algorithm for linear complementarity problems

We present a modified version of the infeasible-interior- We present a modified version of the infeasible-interior-point algorithm for monotone linear complementary problems introduced by Mansouri et al. (Nonlinear Anal. Real World Appl. 12(2011) 545--561). Each main step of the algorithm consists of a feasibility step and several centering steps. We use a different feasibility step, which tar...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Convergence Properties of Hermitian and Skew Hermitian Splitting Methods

In this paper we consider the solutions of linear systems of saddle point problems‎. ‎By using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method‎.

Tight Global Linear Convergence Rate Bounds for Operator Splitting Methods

In this paper we establish necessary and sufficient conditions for linear convergence of operator splitting methods for a general class of convex optimization problems where the associated fixed-point operator is averaged. We also provide a tight bound on the achievable convergence rate. Most existing results establishing linear convergence in such methods require restrictive assumptions regard...