We present a new iterative approach for solving linear systems of equations. Our method is inspired by feedback stabilization schemes from robust control and yields a control system, whose parameters can be tuned to achieve prescribed convergence properties. In contrast to well–known iterative solution methods for linear equations from linear algebra, such as GMRES(m) or Arnoldi’s method, the p...

The aim of this paper is to prove that, in an appropriate setting, every iterative sequence generated by the viscosity approximation method with a sequence of contractions is convergent whenever so is every iterative sequence generated by the Halpern type iterative method. Then, using our results, we show some convergence theorems for variational inequality problems, zero point problems, and fi...

in this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.when the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. additionally for linear feasibil...

Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzuki-type multifunctions.  The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach ...

For Ax = b, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S (α) to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S (α) + K̄ (β) as a preconditioner. We present some com...

Abstract In this paper, we study and analyze an iterative method for solving nonlinear equations with ninth order of convergence. The new proposed method is obtained by composing an iterative method obtained in Noor et al. [9] with Newton’s method and approximating the first-appeared derivative in the last step by a combination of already evaluated function values. The convergence analysis of o...

In this paper, the conjugate direction method is used in designing a type of iterative learning control scheme for a kind of linear discrete time-invariant single-inputsingle-output systems, which is termed as a conjugate direction method based iterative learning control scheme. The convergence of the proposed learning scheme is analyzed by the technique of inductive inference in considering th...

In this work, we study the convergence of an efficient iterative method, the fast sweeping method (FSM), for numerically solving static convex Hamilton–Jacobi equations. First, we show the convergence of the FSM on arbitrary meshes. Then we illustrate that the combination of a contraction property of monotone upwind schemes with proper orderings can provide fast convergence for iterative method...

Convergence of the iterative method based on the successive overrelaxation (SOR) method is investigated to solve the matrix equation in the moment analysis of array antennas. It is found this method can be applied to the sub domain method of moments with fast convergence if the grouping technique is applied and the over-relaxation parameter is properly selected, and the computation time for sol...

In total variation denoising, one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion. Several approaches based on this idea have recently been shown to be very eeective, particularly for denoising functions with discontinuities. This paper analyzes the convergence of an iterative method for solving such problems. The...