Brain Computer Interface (BCI) systems still suffer from lack of accuracy in real-time applications. This problem emerges from isolated optimization, and in some occasions from mismatching of feature extraction and classification stages. To unify optimization of both stages, this paper presents a novel scheme to integrate them and simultaneously optimize under a unit criterion. The proposed method Iteratively estimates both spatio-spectral filters and classifier weights under a non-linear form of Fisher criterion. In order to validate the introduced method, two standard EEG sets, one containing 118 EEG signals and the other 29, were employed to demonstrate its spatial resolution capability. Experimental results on both datasets reveal the superiority of the proposed scheme in terms of enhancing the classification performance simultaneously with speeding up the optimization process, compared to the conventional methods.

In this study based on the accelerated over relaxation (AOR) method we make an Iterative scheme for solving generalized Lyapunov matrix equation AX + XB + Xm j=1 NjXMj = C, over complex or real matrices. Then we analyze the convergence of the new Iterative method in detail. There have been discussions for the calculation of optimal parameters. Finally a numerical example is given to demonstrate the capability of the new method.

In this paper, we proposed a new Iterative process to approximate fixed point of generalized $\alpha$-nonexpansivemappings and show that the coefficient used in the proposed Iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new Iterative process  with other well-known Iterative process by using numerical examples. Finally, by using new Iterative process, we obtained some weak and strong convergence theorems for generalized $\alpha$-nonexpansive mappings in a  Banach space.

The objective of this research is to propose a new multi-step method in tackling a system of nonlinear equations. The constructed Iterative scheme achieves a higher rate of convergence whereas only one LU decomposition per cycle is required to proceed. This makes the e, ciency index to be high as well in contrast to the existing solvers. The usefulness of the presented approach for tackling di, erential equations of nonlinear type with partial derivatives is also given.

Let C be a nonempty closed convex subset of a real Hilbert space H. Let {Sn} and {Tn} be sequences of nonexpansive self-mappings of C, where one of them is a strongly nonexpansive sequence. K. Aoyama and Y. Kimura introduced the iteration process xn+1=bnxn+(1-bn) Sn (anu+(1-an) Tnxn) for finding the common fixed point of {Sn} and {Tn}, where uÎC is an arbitrarily (but fixed) element in C, x0ÎC arbitrarily, {an} and {bn} are sequences in [0; 1]. But in the case where uÏC, the Iterative scheme above becomes invalid because xn may not belong to C. To overcome this weakness, a new Iterative scheme based on the thought of boundary point method is proposed and the strong convergence theorem is proved. As a special case, we can find the minimum-norm common fixed point of {Sn} and {Tn} whether 0ÎC or 0ÏC.

When we discretize nonlinear Volterra integral equations using some numerical, such as collocation methods, the arising algebraic systems are nonlinear. Applying quasilinear technique to the nonlinear Volterra integral equations gives raise to linear Volterra integral equations. The solutions of these equations yield a functional sequence quadratically convergent to the solution. Then, we use collocation method based on Chebyshev polynomials and a modified Clenshaw-Curtis quadrature and obtain a numerical solution. Error analysis has been performed, and the method has been applied on three numerical examples.

We study the convergence of the modified Noor Iterative scheme for the class of asymptotically pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Our results improves, extends and unifies the results of [Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, Mathematical Analysis and Applications, 158 (2) (1991) 407-413] and [Qin et al. Convergence theorems on asymptotically pseudocontractive mappings in the intermediate sense, Fixed Point Theory and Applications, 2010, Article ID 186874, 14 pages, (2010)].