In this paper, a sequential system of linear equations (SSLE) algorithm for solving mathematical problem with linear complementarity constraints is introduced, which uses Fischer-Burmeister (F-B) function and smoothing technique to rewrite CONG ZHANG et al. 150 the complementarity constraints ”. “ 0 0 ≥ ⊥ ≤ w y Under some suitable conditions without upper level complementarity, the proposed met...

The purpose of this paper is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-nonexpansive mappings. The strong convergence theorem is proven in the more general reflexive, strictly convex, and smooth Banach spaces with the property K . The results of this paper improve and extend the results of S. Matsushita and W. Takahashi 2005 ...

We derive a mathematical model for eddy currents in two dimensional geometries where the conductors are thin domains. We assume that the current flows in the x3direction and the inductors are domains with small diameters of order O(ǫ). The model is derived by taking the limit ǫ → 0. A convergence rate of O(ǫα) with 0 < α < 1/2 in the L–norm is shown as well as weak convergence in the W 1,p spac...

A mathematical analysis is performed on a recently reported gradient-based adaptive algorithm named the Euclidean Direction Set (EDS) method. It has been shown that the EDS algorithm has a computational complexity of O(N) for each system update, and a rate of convergence (based on computer simulations) comparable to the RLS algorithm. In this paper, the stability of the EDS method is studied an...

Using fuzzy filters in the sense of P. Eklund and W. Gähler [2], it turns out that fuzzy preuniform convergence spaces introduced in [11] form a strong topological universe in which fuzzy topological spaces as well as fuzzy (quasi) uniform spaces can be studied. Thus, better tools such as the existence of natural function spaces, the existence of one-point extensions (and consequently, the here...

A multigrid preconditioning scheme for solving the Ciarlet-Raviart mixed method equations for the biharmonic Dirichlet problem is presented. In particular, a Schur complement formulation for these equations which yields non-inherited quadratic forms is considered. The preconditioning scheme is compared with a standard W-cycle multigrid iteration. It is proved that a Variable V-cycle preconditio...

The purpose of this paper is to establish the convergence in law of the sequence of “midpoint” Riemann sums for a stochastic process of the form f ′(W ), where W is a Gaussian process whose covariance function satisfies some technical conditions. As a consequence we derive a change-ofvariable formula in law with a second order correction term which is an Itô integral of f ′′(W ) with respect to...

Denoting by S the sharp constant in the Sobolev inequality in W 0 (B), being B the unit ball in R, and denoting by Sh its approximation in a suitable finite element space, we show that Sh converges to S as h ↘ 0 with a polynomial rate of convergence. We provide both an upper and a lower bound on the rate of convergence, and present some numerical results.

In order to solve the convex minimization problem with at least two variables, the augmented Lagrangian method is often used and improved to the alternating direction method of multipliers (ADMM) in the Gauss-Seidel or Jacobian fashion. Though various versions of the ADMM were developed for solving the two-block separable convex problem with linear equality constraint, there are a few feasible ...

A detailed analysis of convergence rate is presented for an iterative path formulated optimal routing algorithm. The primary objective is to quantify, analytically, how the convergence rate changes as the number of nodes in the underlying graph increases. The analysis is motivated by a particular path formulated gradient projection algorithm that has demonstrated excellent convergence rate -. p...