New Iterative Method with Application

In this paper, we consider iterative methods to find a simple root of a nonlinear equation f(x) = 0, where f : D∈R→R for an open interval D is a scalar function.

Iterative Update of a Random Forest Classifier for Diabetic Retinopathy

Random Forests are well-known Machine Learning classification mechanisms based on a collection of decision trees. In the last years, they have been applied to assess the risk of diabetic patients to develop Diabetic Retinopathy. The results have been good, despite the unbalance of data between classes and the inherent ambiguity of the problem (patients with similar data may belong to different classes). In this work we propose a new iterative method to update the set of trees in the Random Forest by considering trees generated from the data of the new patients that are visited in the medical centre. With this method, it has been possible to improve the results obtained with standard Random Forests.

ITERATIVE COMPUTATION FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE SET OF COMMON FIXED POINTS OF QUASI-NONEXPANSIVE AND DEMICONTRACTIVE MAPPINGS

In this paper, a new iterative method for solving convex minimization problems over the set of common fixed points of quasi-nonexpansive and demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. As an application, we shall utilize our results to solve quadratic optimization problems involving bounded linear operator. Our theorems are significant improvements on several important recent results.

Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications

In this article, we discuss the hierarchical fixed point and split monotone variational inclusion problems and propose a new iterative method with the inertial terms involving a step size to avoid the difficulty of calculating the operator norm in real Hilbert spaces. A strong convergence theorem of the proposed method is established under some suitable control conditions. Furthermore, the proposed method is modified and used to derive a scheme for solving the split problems. Finally, we compare and demonstrate the efficiency and applicability of our schemes for numerical experiments as well as an example in the field of image restoration.

New Iterative Method of Solving Nonlinear Equations in Fluid Mechanics

This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed to find an exact solution of the fractional wave equation and fractional Burgers’ equation, as well as an approximate solution of fractional KdV equation and fractional Boussinesq equation. Fractional derivatives of the order α are described using Caputo's definition with 0 < α ≤ 1 or 1 < α ≤ 2. A comparative analysis of the results obtained using a new iterative method with those obtained by the Adomian decomposition method showed the first method to be more efficient and simple, providing accurate results in fewer computational operations. Given its flexibility and ability to solve nonlinear equations, the iterative method can be used to solve more complex linear and nonlinear fractional partial differential equations.

COMPUTATIONAL SOLUTION OF TEMPERATURE DISTRIBUTION IN A THIN ROD OVER A GIVEN INTERVAL I={x├|0

In this paper, two analytical–numerical algorithms are formulated based on homotopy perturbation method and new iterative method to obtain numerical solution for temperature distribution in a thin rod over a given finite interval. The effects of different parameters such as the coefficient which accounts for the heat loss and the diffusivity constant are examined when initial temperature distribution (trigonometry and algebraic functions) are considered. The error in both algorithms approaches to zero as the computational length increases. The proposed algorithms have been demonstrated to be quite flexible, robust and accurate. Thus, the algorithms are established as good numerical tools to solve several problems in applied mathematics and other related field of sciences