Homotopy Perturbation Method and Convergence Analysis for the Linear Mixed Volterra-Fredholm Integral Equations

In this paper, the homotopy perturbation method is presented for solving the second kind linear mixed Volterra-Fredholm integral equations. Then, Aitken method is used to accelerate the convergence. In this method, a series will be constructed whose sum is the solution of the considered integral equation. Convergence of the constructed series is discussed, and its proof is given; the error estimation is also obtained. For more illustration, the method is applied on several examples and programs, which are written in MATLAB (R2015a) to compute the results. The absolute errors are computed to clarify the efficiency of the method.

Multi-User Detection Analysis via Aitken-δ2 EM Acceleration Algorithm

The EM iterative algorithm is commonly used in recent years for missing data, which has the character of easy and popular applicability. But the EM algorithm has a fatal weakness that the convergence speed is slowly; Acceleration of the EM algorithm using the Aitken method is proposed in order to solve this problem.In Multi-user Detection, via this accelerated algorithm, we get a good performance which trends to ML performance, and compared its speed of convergence with the EM algorithm that Aitken-acceleration algorithm has faster convergence than the standard EM algorithm, and we also illustrate the performance of simulation.

A class of methods for tabular interpolation

A generalization of the Neville–Aitken method is described which allows the construction of interpolating functions, other than polynomials, by means of simple recurrence relations. In particular, simple constructions are given for rational functions and trigonometric series which interpolate prescribed function values at non-equispaced positions of the independent variable.Restrictions imposed by requiring the interpolating functions to be invariant under linear transformations of the coordinates are discussed, and application of the technique to the problem of inverse interpolation is also considered.