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For finding a common solution of generalized equilibrium problem, fixed point problem and the zero points of the sum of two operators, a regularization algorithm is established in the framework of real Hilbert spaces. And the strong convergence theorem is obtained under certain assumptions. The main results presented in this paper are useful in nonlinear analysis and optimization. Moreover, the results and corollaries extend the corresponding conclusions proposed by many authors. [ABSTRACT FROM AUTHOR]

An automated general purpose method is introduced for computing a rigorous estimate of a bounded region in ℝ n whose points satisfy a given property. The method is based on calculations conducted in interval arithmetic and the constructed approximation is built of rectangular boxes of variable sizes. An efficient strategy is proposed, which makes use of parallel computations on multiple machines and refines the estimate gradually. It is proved that under certain assumptions the result of computations converges to the exact result as the precision of calculations increases. The time complexity of the algorithm is analyzed, and the effectiveness of this approach is illustrated by constructing a lower bound on the set of parameters for which an overcompensatory nonlinear Leslie population model exhibits more than one attractor, which is of interest from the biological point of view. This paper is accompanied by efficient and flexible software written in C++ whose source code is freely available at . [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new mapping for a finite family of accretive operators and introduce an iterative algorithm for finding a common zero of a finite family of accretive operators in a real reflexive strictly convex Banach space which has a uniformly Gâteaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function invariant on [0, ∞). Furthermore, we prove the strong convergence under some certain conditions. The results obtained in this paper improve and extend the corresponding ones announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a split hierarchical monotone variational inclusion problem (SHMVIP) which includes split variational inequality problems, split monotone variational inclusion problems, split hierarchical variational inequality problems, etc., as special cases. An iterative algorithm is proposed to compute the approximate solutions of an SHMVIP. The weak convergence of the sequence generated by the proposed algorithm is studied. We present an example to illustrate our algorithm and convergence result. [ABSTRACT FROM AUTHOR]

Solving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids. [ABSTRACT FROM AUTHOR]

In the present paper, we propose an iterative algorithm for solving the generalized (P, Q)-reexive solution of the quaternion matrix equation Σul=1 AlXBl + Σvs=1 CsX̃Ds = F. By this iterative algorithm, the solvability of the problem can be determined automatically. When the matrix equation is consistent over a generalized (P, Q)-reexive matrix X, a generalized (P, Q)-reexive solution can be obtained within finite iteration steps in the absence of roundoff errors, and the least Frobenius norm generalized (P, Q)-reexive solution can be obtained by choosing an appropriate initial iterative matrix. Furthermore, the optimal approximate generalized (P, Q)-reexive solution to a given matrix X0 can be derived by finding the least Frobenius norm generalized (P, Q)-reexive solution of a new corresponding quaternion matrix equation. Finally, two numerical examples are given to illustrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]