Iterative Fixed-Point Methods for Solving Nonlinear Problems: Dynamics and Applications

Abstract

and Applied Analysis Volume 2014, Article ID 313061, 2 pages http://dx.doi.org/10.1155/2014/313061 2 Abstract and Applied Analysis α and c whose associated iterative schemes show stable and unstable behavior. W. Zhou and J. Kou present a third-order variant of Potra-Ptak’s iterative method for solving nonlinear systems in Banach spaces, by using a new vector extrapolation technique, whose local and semilocal convergence are proved. In their manuscript, M. J. Martinez et al. use the fixed point iterative scheme to correct the errors between Hipparcos and ICRF2 Celestial catalogues.This allows the authors to link both systems, giving a uniform reference regardless the celestial body (an astronomical radio source) is visible or not. In the manuscript “Existence and Algorithm for the System of Hierarchical Variational Inclusion Problems,” the authors study the existence and approximation of solution of this kind of problems in Hilbert spaces. By using Mainge’s approach, N. Wairojjana and P. Kumam improve and generalize some known results in this area. In the context of iterative methods for solving nonlinear matrix equations, four papers have been presented. M. K. Razavi et al. show a new iterative method for computing the approximate inverse of a nonsingular matrix. Moreover, F. Soleymani et al. describe an iterative process with cubical rate of convergence for finding the principal matrix square root. Application of this approach is illustrated by solving a matrix differential equation. On the other hand, in “An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign,” the authors present a fast algorithm for computing the geometric mean of twomatrices of this specific type. Finally, in “Approximating the Matrix Sign Function Using a Novel Iterative Method,” the authors present an iterative method for finding the sign of a square complex matrix. L. Guo et al. use the reproducing kernel iterative method to solve a class of two-point boundary value problems. By homogenizing the boundary conditions, the two-point boundary value problems are converted into the equivalent nonlinear operator equation. They prove that both solutions are equivalent and show the analysis of error and the numerical stability of the method. In “Existence of Solutions for a Coupled Systemof Second and Fourth Order Elliptic Equations,” the author generalizes quasilinearization technique to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of this kind of systems. Finally, in “TheHybrid Steepest DescentMethod for Split Variational Inclusion and Constrained ConvexMinimization Problems,” the authors introduce new implicit and new explicit iterative schemes for finding a common element of the set of solutions of a constrain convex minimization problems and the set of solutions of the split variational inclusion problem.