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The main goal of this paper is to study the order of convergence and the efficiency of four families of iterative methods using frozen divided differences. The first two families correspond to a generalization of the secant method and the implementation made by Schmidt and Schwetlick. The other two frozen schemes consist of a generalization of Kurchatov method and an improvement of this method applying the technique used by Schmidt and Schwetlick previously. An approximation of the local convergence order is generated by the examples, and it numerically confirms that the order of the methods is well deduced. Moreover, the computational efficiency indexes of the four algorithms are presented and computed in order to compare their efficiency. [ABSTRACT FROM AUTHOR]

The paper presents iterative methods for calculating the neutron flux distribution in nonlinear problems of nuclear reactor criticality. Algorithms for solving equations for variations in the neutron flux are considered. Convergence of the iterative processes is studied for two nonlinear problems in which macroscopic interaction cross sections are functionals of the spatial neutron distribution. In the first problem, the neutron flux distribution depends on the water coolant density, and in the second one, it depends on the fuel temperature. Simple relationships connecting the vapor content and the temperature with the neutron flux are used. [ABSTRACT FROM AUTHOR]

Constraint preconditioners have proved very efficient for the solution of ill-conditioned finite element (FE) coupled consolidation problems in a sequential computing environment. Their implementation on parallel computers, however, is not straightforward because of their inherent sequentiality. The present paper describes a novel parallel inexact constraint preconditioner (ParICP) for the efficient solution of linear algebraic systems arising from the FE discretization of the coupled poro-elasticity equations. The ParICP implementation is based on the use of the block factorized sparse approximate inverse incomplete Cholesky preconditioner, which is a very recent and effective development for the parallel preconditioning of symmetric positive definite matrices. The ParICP performance is experimented with in real 3D coupled consolidation problems, proving a scalable and efficient implementation of the constraint preconditioning for high-performance computing. ParICP appears to be a very robust algorithm for solving ill-conditioned large-size coupled models in a parallel computing environment. [ABSTRACT FROM AUTHOR]

In this paper, we use the auxiliary principle technique to suggest and analyze an implicit iterative method for solving bifunction variational inequalities. We also study the convergence criteria of this new method under pseudomonotonicity condition. [ABSTRACT FROM AUTHOR]

In this paper we show that an iterative sequence generated by the Halpern algorithm converges to a fixed point in the case of complete CAT( κ) spaces. Similar results for Hadamard manifolds were obtained in [Li, C., López, G., Martín-Márquez, V.: Iterative algorithms for nonexpansive mappings on Hadamard manifolds. Taiwanese J. Math., 14, 541-559 (2010)], but we study a much more general case. Moreover, we discuss the Halpern iteration procedure for set-valued mappings. [ABSTRACT FROM AUTHOR]

Many optimization problems reduce to the solution of a system of linear inequalities (SLI). Some solution methods use relaxed, averaged projections. Others invoke surrogate constraints (typically stemming from aggregation). This paper proposes a blend of these two approaches. A novelty comes from introducing as surrogate constraint a halfspace defined by differences of algorithmic iterates. The first iteration is identical to surrogate constraints methods. In next iterations, for a given approximation x¯, besides the violated constraints in x¯, we also take into consideration the surrogate inequality, which we have obtained in the previous iteration. The motivation for this research comes from the recent work of Scolnik et al. (Appl. Numer. Math. 41, 499—513, 2002), who studied some projection methods for a system of linear equations. [ABSTRACT FROM AUTHOR]