Iterative splitting methods have a huge amount to compute matrix exponential. Here, the acceleration and recovering of higher-order schemes can be achieved. From a theoretical point of view, iterative splitting methods are at least alternating Picards fix-point iteration schemes. For practical applications, it is important to compute very fast matrix exponentials. In this paper, we concentrate ...

In this paper , we study the strong convergence of SP iterative scheme for quasi-contractive operators in Banach spaces. We show that Picard , Mann , Ishikawa , Noor, new two step and SP iterative schemes are equivalent for quasi-contractive operators. In addition, we show that the rate of convergence of SP iterative scheme is better than the other iterative schemes mentioned above for increasi...

In this paper, we discuss in time domain the convergence of the iterative process for fractional-order systems. Fractional order iterative learning updating schemes are considered. The convergent conditions of the fractional-order and integer-order iterative learning schemes are proved to be equivalent. It is shown in Matlab/Simulink results that the tracking speed is the fastest when the syste...

The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...

The oscillations of a centered second order nite diierence scheme and the excessive diiusion of a rst order centered scheme can be overcome by global composition of the two, that is by performing cycles consisting of several time steps of the second order method followed by one step of the diiusive method. We show the eeectiveness of this approach on some test problems in two and three dimensions.

The paper iterates on the observation made independently by several groups of authors that building subdivision schemes out of simple, very local and geometrically invariant averaging rules is convenient both from a theoretical and practical point of view. We review the benefits of this approach with special emphasis on the smoothness analysis of the limit surfaces, derive certain guidelines fo...