Recasting this in the form above we have 1 B M N − = − and . 1 c M b − = It is easy to show that this iteration is consistent for any splitting as long as M is nonsingular. Obviously, to be practical the matrix M must be selected so that the system My d = is easily solved. Popular choices for M are diagonal matrices (as in the Jacobi method), lower triangular matrices (as in the Gauss-Seidel an...

A parallel inexact Newton method with a line search is proposed for two-stage quadratic stochastic programs with recourse. A lattice rule is used for the numerical evaluation of multi-dimensional integrals, and a parallel iterative method is used to solve the quadratic programming subproblems. Although the objective only has a locally Lipschitz gradient, global convergence and local superlinear...

This work presents the use of local fuzzy prototypes as a new idea to obtain accurate local semantics-based Takagi–Sugeno–Kang ~TSK! rules. This allow us to start from prototypes considering the interaction between input and output variables and taking into account the fuzzy nature of the TSK rules. To do so, a two-stage evolutionary algorithm based on MOGUL ~a methodology to obtain Genetic Fuz...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

This paper introduces a new modification to an iterative method for solving Cauchy problems (IVPs) based on inverse polynomial technique. The proposed is proven be consistent, stable, and convergent. We also demonstrate the consistency property of One-stage scheme Two-stage scheme, as well stability method. To validate accuracy our approach, we conduct several numerical experiments present resu...

A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of Newton multi-step method. The auxiliary function provides us the way to overcome the singul...

In this paper, we proposed a fast and accurate human pose estimation framework that combines top-down and bottom-up methods. The framework consists of an initialization stage and an iterative searching stage. In the initialization stage, example based method is used to find several initial poses which are used as searching seeds of the next stage. In the iterative searching stage, a larger numb...