Singular systems with index one arise in many applications, such as Markov chain modelling. In this paper, we use the group inverse to characterize the convergence and quotient convergence properties of stationary iterative schemes for solving consistent singular linear systems when the index of the coefficient matrix equals one. We give necessary and sufficient conditions for the convergence o...

A preconditioned AOR iterative method is proposed with the preconditioner I + S∗ αβ. Some comparison theorems are given when the coefficient matrix of linear system A is an irreducible L−matrix. The convergence rate of AOR iterative method with the preconditioner I + S∗ αβ is faster than the convergence rate with the preconditioner I + Sα by Li et al. Numerical example verifies comparison theor...

In this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given.

The aim of this paper is to construct an e¢ cient iterative method to solve nonlinear equations. This method is obtained from M. Javidi’s method (Appl. Math. Comput. 193 (2007) 360-365), which is third-order. The convergence order of new method is established to six and the e¢ ciency index is 1.5651. The Proposed method is compared with the second, third and sixth order methods. Some numerical ...

GPBiCG method is an attractive iterative method for the solution of a linear system of equations with nonsymmetric coefficient matrix. However, we meet often with instability of convergence when GPBiCG method is adopted in the solution of realistic problems. In this paper, we consider a new algorithm with minimization of the associate residual and without reverse-ordered recurrence in the algor...

In this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent to the fixed point of a single-valued contraction operator. Then we make the comparison of their rate of convergence. Additionally, numerical examples for these iteration processes are given.

The construction of initial conditions of an iterative method is one of the most important problems in solving nonlinear equations. In this paper, we obtain relationships between different types of initial conditions that guarantee the convergence of iterative methods for simultaneous finding all zeros of a polynomial. In particular, we show that any local convergence theorem for a simultaneous...

Modification of Newtons method with higher-order convergence is presented.The modification of Newtons method is based on Frontinis three-order method The new method requires two-step per iteration. Analysis of convergence demonstrates that the order of convergence is 6. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and ...

In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern,  Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper...

A new iterative learning controller is proposed for a general unknown discrete time-varying nonlinear non-affine system represented by NARMAX (Nonlinear Autoregressive Moving Average with eXogenous inputs) model. The proposed controller is composed of an iterative learning neural identifier and an iterative learning controller. Iterative learning control and iterative learning identification ar...