This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing the sum of the l1-norms that correspond to each basis, which is a tractable convex approach. We find novel optimality conditions which indicates a gain over...

In recent years several papers have appeared investigating the classical discrete logarithm problem for elliptic curves by means of the multivariate polynomial approach based on the celebrated summation polynomials, introduced by Semaev in 2004. However, with a notable exception by Petit et al. in 2016, all numerous papers have investigated only the composite-field case, leaving apart the labor...

Radial basis functions are a very powerful tool in multivariate approximation since they are mesh free. In the theory of radial basis functions, the most frequently used error bounds are the one raised by Madych and Nelson in [5] and the one raised by Wu and Schaback in [6], especially the latter. It seems that Wu and Schaback’s error bound is five times more frequently used than that of Madych...

This paper, two Artificial Neural Network (ANN) models using radial basis function (RBF) nets are developed for the design of Aperture Coupled Microstrip Antennas (ACMSA) for different number of design parameters. The effect of increasing the number of design parameters on the ANN model is also discussed in this work. The performances of the models when compared are found that on decreasing the...

The goal of this study is the automatic construction of a vectorial polynomial basis for Nédélec mixed finite elements [7], particular, the generation of finite elements without the expression of the polynomial basis functions, using symbolic calculus: the exhibition of basis functions has no practical interest.

In this paper, a modied version of LLL algorithm, which is a an algorithm with output-sensitivecomplexity, is presented to convert a given Grobner basis with respect to a specic order of a polynomialideal I in arbitrary dimensions to a Grobner basis of I with respect to another term order.Also a comparison with the FGLM conversion and Buchberger method is considered.

This paper deals with continuous frames and continuous Riesz bases. We introduce continuous Riesz bases and give some equivalent conditions for a continuous frame to be a continuous Riesz basis. It is certainly possible for a continuous frame to have only one dual. Such a continuous frame is called a Riesz-type frame [13]. We show that a continuous frame is Riesz-type if and only if it is a con...

AhtractThis paper discusses the rationale for employing alternative basis functions to the ubiquitous Gaussian in Radial Basis Function networks. In particular we concentrate upon employing unbounded basis functions (though the network as a whole remains bounded), and non positive definite basis functions. The use of unbounded and nonpositive basis functions, though counterintuitive in applicat...

a generalization of schauder basis associated with the concept of generalized analytic functions is introduced. corresponding concepts of density, completeness, biorthogonality and basicity are defined. also, corresponding concept of the space of coefficients is introduced. under certain conditions for the  corresponding operators, some properties of the space of coefficients and basicity crite...

The dynamic problems of a microactuator with a single edge crack are numerically formulated using radial basis functions. The microactuator model incorporates the taper ratio, electrode shapes, and crack length, all of which govern the dynamic behavior of microactuators. To optimize the design of a microactuator, many characteristics of various shaped cantilevers and curved electrodes are also ...