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Abstract: Multipoint iterative methods belong to the class of the most efficient methods for solving nonlinear equations. Recent interest in the research and development of this type of methods has arisen from their capability to overcome theoretical limits of one-point methods concerning the convergence order and computational efficiency. This survey paper is a mixture of theoretical results and algorithmic aspects and it is intended as a review of the most efficient root-finding algorithms and developing techniques in a general sense. Many existing methods of great efficiency appear as special cases of presented general iterative schemes. Special attention is devoted to multipoint methods with memory that use already computed information to considerably increase convergence rate without additional computational costs. Some classical results of the 1970s which have had a great influence to the topic, often neglected or unknown to many readers, are also included not only as historical notes but also as genuine sources of many recent ideas. To a certain degree, the presented study follows in parallel main themes shown in the recently published book (Petković et al., 2013) [53], written by the authors of this paper. [Copyright &y& Elsevier]

In this paper, we investigate the nonlinear matrix equations X + A * X q A = Q ( 0 < q ≤ 1 ) and X − A * X q A = Q ( q > 1 ) . Necessary and sufficient conditions for the (unique) existence of Hermitian positive definite solutions of these equations are derived. Effective iterative algorithms are also provided to obtain the unique solution of X + A * X q A = Q ( 0 < q ≤ 1 ) and the minimal and maximal Hermitian positive definite solutions of X − A * X q A = Q ( q > 1 ) . Numerical examples are included to illustrate the efficiency of the presented iteration algorithms. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider numerical simulation to a class of constrained dynamic problems where the overall dynamics are determined by the interactions between two sub-systems. We present an iterative algorithm that naturally decouples the computation of the two sub-systems and that ensures an accurate and efficient solution procedure. We conduct rigorous error analysis for the convergence of the iterative algorithm, and verify the analytical results through careful numerical tests. [Copyright &y& Elsevier]

Abstract: In this paper we propose an iterative algorithm to solve large size linear inverse ill posed problems. The regularization problem is formulated as a constrained optimization problem. The dual Lagrangian problem is iteratively solved to compute an approximate solution. Before starting the iterations, the algorithm computes the necessary smoothing parameters and the error tolerances from the data. The numerical experiments performed on test problems show that the algorithm gives good results both in terms of precision and computational efficiency. [Copyright &y& Elsevier]

Abstract: In this paper, the issue of multi-degree reduction of Bézier curves with C 1 and G 2-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method. [Copyright &y& Elsevier]

Abstract: In this paper two algorithms for computing the principal square root of a centrosymmetric H-matrix with positive diagonal entries are proposed. It is showed that our algorithms ensure significant savings in computational costs, as compared to the case of an arbitrary H-matrix A with positive diagonal entries. [Copyright &y& Elsevier]