In this paper, an iterative method was considered for solving the absolute value equation (AVE). We suggest a two-step in which well-known Gauss quadrature rule is corrector step and generalized Newton taken as predictor step. The convergence of proposed established under some acceptable conditions. Numerical examples prove consistency capability new method.

ABS methods are direct iterative methods for solving linear systems of equations, where the i-th iteration satisfies the first i equations. Thus, a system of m equations is solved in at most m ABS iterates. In 2004 and 2007, two-step ABS methods were introduced in at most [((m+1))/2] steps to solve full row rank linear systems of equations. These methods consuming less space, are more compress ...

Image restoration is an ill-posed inverse problem, which has been introduced the regularization method to suppress over-amplification. In this paper, we propose to apply the iterative regularization method to the image restoration problem and present a nested iterative method, called iterative conjugate gradient regularization method. Convergence properties are established in detail. Based on [...

The aim of this article is to describe the formulation of the quarter-sweep iterative alternating decomposition explicit (QSIADE) method using the finite difference approach for solving one-dimensional diffusion equations. The concept of the QSIADE method is inspired via combination between the quarter-sweep iterative and the iterative alternating decomposition explicit (IADE) methods known as ...

Abstract In this paper, a new class of generalized nonlinear complementarity problems is introduced and studied, and an iterative algorithm, called the three-step iteration scheme with errors, is suggested. The existence and uniqueness of solution for the generalized nonlinear complementarity problem and the convergence, stability and weak stability of iterative sequence generated by the algori...

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the proposed iterative scheme under some appropriate conditions.

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the proposed iterative scheme under some appropriate conditions.

The 2D absolute phase estimation problem, in interferometric applications, is to infer absolute phase (not simply modulo-2π) from incomplete, noisy, and modulo-2π image observations. This is known to be a hard problem as the observation mechanism is nonlinear. In this paper we adopt the Bayesian approach. The observation density is 2π-periodic and accounts for the observation noise; the a prior...

We present new algorithms for parameter estimation of HMMs. By adapting a framework used for supervised learning, we construct iterative algorithms that maximize the likelihood of the observations while also attempting to stay “close” to the current estimated parameters. We use a bound on the relative entropy between the two HMMs as a distance measure between them. The result is new iterative t...

Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed at each iteration step by a suitable approximation process, e.g., by GMRES itself.