A preconditioned gradient-based iterative method is derived by judicious selection of two auxiliary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence o...

The well known LBG algorithm uses binary splitting method for generating initial codebook which is then iteratively improved by GLA. In the present paper we study different variants of the splitting method and its application to codebook generation problem with and without GLA. A new iterative splitt ing method is proposed which is applicable to the codebook generation without the use of GLA. E...

In this paper, a new multi-parameter iterative algorithm is proposed to address the PageRank problem based on multi-splitting iteration method. The method solves two linear subsystems at each by splitting coefficient matrix, considering therefore inner and outer find approximate solutions of these subsystems. It can be shown that sequence generated finally converges vector when parameters satis...

How to accelerate the convergence speed and avoid computing inversion of a Jacobian matrix is important in solution nonlinear algebraic equations (NAEs). This paper develops an approach with splitting-linearizing technique based on term reduce effect terms. We decompose terms NAEs through splitting parameter then linearize around values at previous step linear system. Through maximal orthogonal...

In this paper, the split fixed point and variational inclusion problem is considered. With help of technique, Tseng-type splitting method self-adaptive rule, an iterative algorithm proposed for solving in which involved operators S T are demicontractive g plain monotone. Strong convergence theorem proved under some mild conditions.

We discuss iterative operator-splitting methods for convection-diffusion and wave equations motivated from the eigenvalue problem to decide the splitting process. The operator-splitting methods are well-know to solve such complicated multi-dimensional and multi-physical problems. Often the problem, how to decouple the underlying operators, is not understood well enough. We propose a method base...

In this paper, we numerically simulated a glass-based all-optical 1×N power splitter with eleven different configurations using soliton breakup in a nonlinear medium. It is shown that in addition to reconfigurability of the proposed splitter, its power splitting ratio is tunable up to some extent values too. Nonlinear semivectorial iterative finite difference beam propagation method (IFD-...

Over the years, many methods for solving the linear complementarity problem (LCP) have been developed. Most of these methods have their origin in solving a system of linear equations. In particular, much attention has recently been paid on the class of iterative methods called the splitting method, which is an extension of the matrix splitting method for solving a system of linear equations suc...

In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov?s regularization. regularization process, we convert well-posed system. The convergence such discussed by using different types splittings. Comparison analysis both systems are studied operating certain weak Further, have extended double [Song J. and Song Y, Calcolo 48(3), 2...