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In this manuscript we suggest a fast adaptive distributed method for maximum likelihood APPROXIMATION (MLA) in multiple view object localization problem. For this purpose, we use "up to scale" property of projective geometry and by defining coefficients for convergence criterion, we increase the convergence speed of the consensus algorithm. We try to present a mathematical model for the problem. We use two types of error function. The proposed method uses maximum likelihood for obtaining its best parameters. Our approach utilizes "up to scale" property in projective geometry to reach the consensus quickly. The difference between nodes' values and meanwhile consensus values are evaluated by two error functions. To estimate consensus value in the second error function, we used local weighted average of each node. At the last of the paper, we prove our claims by experimental results.

We will relate the degree of rational APPROXIMATION of a meromorphic function f to the minimum value, on the natural boundary of f, of Green potential of the weak* limit of the normalized pole-counting measures.

Purpose: The purpose of this work is to present an APPROXIMATION for singular integrals of Cauchy type kernel on a smooth-oriented contour.Methods: For the method, we use a small modification of the spline functions in order to eliminate the singularity. Noting that this APPROXIMATION is due to the idea of Sanikidze’s Approximate solution of singular integral equations in the case of closed contours of integrations.Results: This APPROXIMATION represents a good approach for any singular integral given on the curve in the sense of Cauchy principal value.Conclusions: This APPROXIMATION is destined to solve numerically the singular integral equations with Cauchy type kernel on a smooth-oriented contour.

This paper studies the problem of Simultaneous Sparse APPROXIMATION (SSA). This problem arises in many applications that work with multiple signals maintaining some degree of dependency, e. g., radar and sensor networks. We introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion of the convergence of our method, called Simultaneous Iterative Method (SIM). In this study, we compared our method with other group-sparse reconstruction techniques, namely Simultaneous Orthogonal Matching Pursuit (SOMP) and Block Iterative Method with Adaptive Thresholding (BIMAT), through numerical experiments. The simulation results demonstrated that SIM outperformed these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIM is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems.

In this paper, we consider the width invariant trapezoidal and triangular APPROXIMATIONs of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new APPROXIMATION methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed APPROXIMATIONs of fuzzy numbers preserve the expected value too.