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.

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.

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.

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.

In this paper, we introduce a three-step Iterative scheme, called the MF-iteration process to approximate a common fixed point for a hybrid pair $\{\tau, T\}$  of single-valued and multi-valued maps satisfying a generalized contractive condition defined on uniformly convex Banach spaces. We establish the strong convergence theorem for the proposed process under some basic boundary conditions. We give a numerical example to prove our results' convergence rate. Further, we compare the convergence speed of Sokhuma and Kaewkhao [29] and MF-iterations. we show numerically that the considered Iterative scheme converges faster than Sokhuma and Kaewkhao [29] for single-valued and multi-valued non-expansive mappings. Our newly proven results generalize several relevant results in the literature.

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.

Using suitable coordinate systems in CFD have been of interest for many researchers. The objective of this study is numerical modeling of supersonic flows, using a new coordinate system, i.e. Unified coordinate system (UCS) and Iterative Riemann problem solution. Unified coordinate system has advantage over traditional coordinate systems (Eulerian/Lagrangian) in supersonic flows, especially in discontinuous regions (shocks and expansions). Moreover, most of the difficulties of the traditional coordinate system may be removed using UCS. For 2-D gas dynamics calculations in UCS, it is required to approximate fluxes on cell faces. This is normally modeled by Riemann problem solution. It is important to mention that in using UCS, there is no need to generate a body-fitted mesh prior to computing flow past a body, the grid is automatically generated by the flow. The UCS has the advantages of both Eulerian and Lagrangian systems. These can be seen in our results, which also show the high speed in our computations.