Iterative Method For Finding Research Articles

A slight look on a new fixed-point problem

ABSTRACT Nonexpansive mappings and iterative methods for finding their fixed points are an ongoing topic that receives a lot of attention from various areas such that nonlinear analysis and optimization. In this paper, we leverage the connections between nonexpansive mappings, resolvent of maximal monotone operators, and proximal mappings of proper closed convex functions to introduce a new fixed-point problem, propose some algorithms, based on Krasnoselski–Mann and Halpern's iteration methods. Then, we provide some related convergence results and we translate the analysis developed in DC-optimization problems and some non-monotone inclusions.

Approximate solution of nonlinear fuzzy Fredholm integral equations using bivariate Bernstein polynomials with error estimation

<abstract><p>This paper is concerned with obtaining approximate solutions of fuzzy Fredholm integral equations using Picard iteration method and bivariate Bernstein polynomials. We first present the way to approximate the value of the multiple integral of any fuzzy-valued function based on the two dimensional Bernstein polynomials. Then, it is used to construct the numerical iterative method for finding the approximate solutions of two dimensional fuzzy integral equations. Also, the error analysis and numerical stability of the method are established for such fuzzy integral equations considered here in terms of supplementary Lipschitz condition. Finally, some numerical examples are considered to demonstrate the accuracy and the convergence of the method.</p></abstract>

A family of fifth-order iterative methods for finding multiple roots of nonlinear equations

A family of fifth-order iterative methods for finding multiple roots of nonlinear equations

The Picard-HSS-SOR iteration method for absolute value equations

In this paper, we present the Picard-HSS-SOR iteration method for finding the solution of the absolute value equation (AVE), which is more efficient than the Picard-HSS iteration method for AVE. The convergence results of the Picard-HSS-SOR iteration method are proved under certain assumptions imposed on the involved parameter. Numerical experiments demonstrate that the Picard-HSS-SOR iteration method for solving absolute value equations is feasible and effective.

Local and Semilocal Convergence of Nourein’s Iterative Method for Finding All Zeros of a Polynomial Simultaneously

In 1977, Nourein (Intern. J. Comput. Math. 6:3, 1977) constructed a fourth-order iterative method for finding all zeros of a polynomial simultaneously. This method is also known as Ehrlich’s method with Newton’s correction because it is obtained by combining Ehrlich’s method (Commun. ACM 10:2, 1967) and the classical Newton’s method. The paper provides a detailed local convergence analysis of a well-known but not well-studied generalization of Nourein’s method for simultaneous finding of multiple polynomial zeros. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with verifiable initial condition and a posteriori error bound) for the classical Nourein’s method. Each of the new semilocal convergence results improves the result of Petković, Petković and Rančić (J. Comput. Appl. Math. 205:1, 2007) in several directions. The paper ends with several examples that show the applicability of our semilocal convergence theorems.

On weak and strong convergence results for generalized equilibrium variational inclusion problems in Hilbert spaces

We introduce a new iterative method for finding a common element of the set of fixed points of pseudo-contractive mapping, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. We provide some results about strongly and weakly convergent of the iterative scheme sequence to a point pin varOmega which is the unique solution of a variational inequality, where Ω is an intersection of set as given by {varOmega }=F(S)cap (A+B)^{-1}(0) cap N^{-1}(0)cap operatorname{GEP}(F,M)neq emptyset . This gives us a common solution. Also, We show that our results extend some published recent results in this field. Finally, we provide an example to illustrate our main result.

General iterative method for solving fixed point problems involving a finite family of demicontractive mappings in Banach spaces

The purpose of this paper is to study the general iterative method for demicontractive mappings in Banach spaces. The method gives us a~strong convergence iteration for a~finite family of demicontractive mappings and also permits us to solve variational inequality problems involving accretive operators without any compactness condition. Finally, we provide some applications, and an illustration of the proposed method is given in \(l_4\) spaces. Our results improve many recent results using the general iterative method for finding the fixed points of nonlinear operators.

Common solution to generalized mixed equilibrium problem and fixed point problems in Hilbert space

In this paper, we deal with an extra-gradient iterative method for finding a common solution to a generalized mixed equilibrium problem and fixed point problems for a nonexpansive mapping and for a finite family of k-strict pseudo-contraction mappings in Hilbert space. We prove a strong convergence theorem for the extra-gradient iterative method under some mild conditions. Further, we give a numerical example to illustrate the main result.

Approximate solution of zero point problem involving H-accretive maps in Banach spaces and applications

In this manuscript, we introduce two iterative methods for finding the common zeros of two H-accretive mappings in uniformly smooth and uniformly convex Banach spaces. The proposed iterative methods are based on Mann and Halpern iterative methods and viscosity approximation method. Strong convergence results are established for iterative algorithms. Applications based on convex minimization problem, variational inequality problem and equilibrium problem are derived from the main result. Numerical implementation of the main results and application are demonstrated by some examples. Our results extend, generalize, and unify the previously known results given in literature.

Parallel hybrid viscosity method for fixed point problems, variational inequality problems and split generalized equilibrium problems

In this paper, we first propose a new parallel hybrid viscosity iterative method for finding a common element of three solution sets: (i) finite split generalized equilibrium problems; (ii) finite variational inequality problems; and (iii) fixed point problem of a finite collection of demicontractive operators. And we prove that the sequence generated by the iterative scheme strongly converges to a common solution of the above-mentioned problems. Also, we present numerical examples to demonstrate the effectiveness of our algorithm. Our results presented in this paper improve and extend many recent results in the literature.

Sampling and Estimating the Waveform of Analog Signals Based on Precision Event Timing

In this paper, we investigate specific features of compressed sensing methods when estimating the waveform of arbitrary analog signals based on zero-crossings of a signal summed with a periodic oscillation. An algorithm for estimating the waveform of an analog signal with the adaptation of the basis matrix to its spectrum is proposed. To solve the problem of off-grid frequencies, we employ an iterative method for finding the maxima of the spectral peaks between the nodes of a DFT frequency grid.

Newton flows for elliptic functions III & IV

An elliptic Newton flow is a dynamical system that can be interpreted as a continuous version of Newton’s iteration method for finding the zeros of an elliptic function f. Previous work focuses on structurally stable flows (i.e., the phase portraits are topologically invariant under perturbations of the poles and zeros for f), including a classification/representation result for such flows in terms of Newton graphs (i.e., cellularly embedded toroidal graphs fulfilling certain combinatorial properties). The present paper deals with non-structurally stable elliptic Newton flows determined by pseudo Newton graphs (i.e., cellularly embedded toroidal graphs, either generated by a Newton graph, or the so-called nuclear Newton graph, exhibiting only one vertex and two edges). Our study results into a deeper insight in the creation of structurally stable Newton flows and the bifurcation of non-structurally stable Newton flows. As it requires the classification of all third order Newton graphs, we present this classification.

Strong convergence of an iterative algorithm involving nonlinear mappings of nonexpansive and accretive type

ABSTRACTIn this paper, a new iterative method for finding the projection onto the intersection of two closed convex sets in the framework of Banach spaces is presented. It is a viscosity approximation method which produces a strongly convergent sequence.

A simple efficient method for solving sixth-order nonlinear boundary value problems

In this paper, we propose a simple efficient method for a sixth-order nonlinear boundary value problem. It is based on the reduction of the problem to an operator equation for the right-hand-side function. The existence and uniqueness of a solution and its positivity are established. An iterative method for finding the solution is investigated. A numerical realization of the iterative method with the use of a difference scheme of sixth-order accuracy shows the efficiency and advantages of the proposed method over some other methods.

Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the iterative scheme. Finally, we derive some consequences from our main result. Our work is an improvement and extension of some previously known results recently obtained by many authors.

Slow Growth of a Crack with Contacting Faces in a Viscoelastic Body

An algorithm for solving the problem of slow growth of a mode I crack with a zone of partial contact of the faces is proposed. The algorithm is based on a crack model with a cohesive zone, an iterative method of finding a solution for the elastic opening displacement, and elasto–viscoelastic analogy, which makes it possible to describe the time-dependent opening displacement in Boltzmann–Volterra form. A deformation criterion with a constant critical opening displacement and cohesive strength during quasistatic crack growth is used. The algorithm was numerically illustrated for tensile loading at infinity and two concentrated forces symmetric about the crack line that cause the crack faces to contact. When the crack propagates, the contact zone disappears and its dynamic growth begins.

A shrinking projection extragradient algorithm for equilibrium problem and fixed point problem

In this paper, a shrinking projection algorithm based on the extragradient iteration method for finding a common element of the set of common fixed points of a finite family of asymptotically nonexpansive mappings and a generalized nonexpansive set-valued mapping and the set of solutions of equilibrium problem for pseudomonotone and Lipschitz-type continuous bifunctions is introduced and investigated in Hilbert spaces. Moreover, the strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results in this field.

Weak convergence theorem for variational inequality problems with monotone mapping in Hilbert space

We know that variational inequality problem is very important in the nonlinear analysis. The main purpose of this paper is to propose an iterative method for finding an element of the set of solutions of a variational inequality problem with a monotone and Lipschitz continuous mapping in Hilbert space. This iterative method is based on the extragradient method. We get a weak convergence theorem. Using this result, we obtain three weak convergence theorems for the equilibrium problem, the constrained convex minimization problem, and the split feasibility problem.

The split common fixed point problem for asymptotically nonexpansive semigroups in Banach spaces

In this paper, we propose an iteration method for finding a split common fixed point of asymptotically nonexpansive semigroups in the setting of two Banach spaces, and we obtain some weak and strong convergence theorems of the iteration scheme proposed. The results presented in the paper are new and improve and extend some recent corresponding results.

A New Accurate and Efficient Iterative Numerical Method for Solving the Scalar and Vector Nonlinear Equations: Approach Based on Geometric Considerations

This paper deals with a new numerical iterative method for finding the approximate solutions associated with both scalar and vector nonlinear equations. The iterative method proposed here is an extended version of the numerical procedure originally developed in previous works. The present study proposes to show that this new root-finding algorithm combined with a stationary-type iterative method (e.g., Gauss-Seidel or Jacobi) is able to provide a longer accurate solution than classical Newton-Raphson method. A numerical analysis of the developed iterative method is addressed and discussed on some specific equations and systems.