We propose a fast and stable numerical method to evaluate two-dimensional partial differential equation (PDE) for pricing arithmetic average Asian options. The numerical method is deduced by combining an alternating-direction technique and the central difference scheme on a piecewise uniform mesh. The numerical scheme is stable in the maximum norm, which is true for arbitrary volatility and arb...

In this paper, an unconditionally stable three-dimensional (3-D) finite-difference time-method (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy. The principle of the alternating direction implicit (ADI) technique that has been used in formulating an unconditionally stable two-dimensional FDTD is applied. Unlike the conventional ADI algorithms, ho...

Knowing the fact that the main weakness of the most standard methods including k-means and hierarchical data clustering is their sensitivity to initialization and trapping to local minima, this paper proposes a modification of convex data clustering  in which there is no need to  be peculiar about how to select initial values. Due to properly converting the task of optimization to an equivalent...

With the explosive growth in demand for mobile data traffic, contradiction between capacity requirements and spectrum scarcity becomes more prominent. The bandwidth is becoming a key issue 5G networks. However, with huge from 30 GHz to 300 GHz, mm Wave communications considered an important part of network providing multi communication services, where channel state information considers challen...