in many industrialized areas, the highest concentration of particulate matter, as a major concern on public health, is being felt worldwide problem. since the air pollution assessment and its evaluation with considering spatial dispersion analysis because of various factors are complex, in this paper, gis-based modeling approach was utilized to zoning pm2.5 dispersion over tehran, during one ye...

In this paper, we identify univariate prewavelets on spaces spanned by translates of multiquadric functions and other radial basis functions with nonequally spaced centers (or "knots"). Although the multiquadric function and its relations are our prime examples, the theory is sufficiently broad to admit prewavelets from other radial basis function spaces as well.

This note concerns density properties of the general multiquadric, (x + c2)k−1/2, where k is a fixed natural number. We establish that scattered translates of the general multiquadric are dense in C([a, b]), where a and b are finite. As a corollary, we show that scattered translated of the general multiquadric are dense in the function spaces L([a, b]), for 1 ≤ p <∞.

It’s well-known that there is a so-called high-level error bound for multiquadric and inverse multiquadric interpolations, which was put forward by Madych and Nelson in 1992. It’s of the form |f(x)− s(x)| ≤ λ 1 d ‖f‖h where 0 < λ < 1 is a constant, d is the fill distance which roughly speaking measures the spacing of the data points, s(x) is the interpolating function of f(x), and h denotes the...

A generalised multiquadric radial basis function is a function of the form s(x) = ∑N i=1 diφ(|x − ti|), where φ(r) = ( r2 + τ2 )k/2 , x ∈ Rn, and k ∈ Z is odd. The direct evaluation of an N centre generalised multiquadric radial basis function at m points requires O(mN) flops, which is prohibitive when m and N are large. Similar considerations apparently rule out fitting an interpolating N cent...

This paper presents numerical solution of elliptic partial differential equations Poisson’s equation using a combination of logarithmic and multiquadric radial basis function networks. This method uses a special combination between logarithmic and multiquadric radial basis functions with a parameter r. Further, the condition number which arises in the process is discussed, and a comparison is m...

Radial Basis Function networks with linear output are often used in regression problems because they can be substantially faster to train than Multi-layer Perceptrons. We show how radial base Cauchy, multiquadric and Inverse multiquadric type functions can be used to approximate a rapidly changing continuous test function. In this paper, the performance of the reduced matrix design by QLP decom...

Some researchers have presented the application of radial basis function approximation to the evaluation of option contracts. In a previous study, the authors described the evaluation of Asian options by using radial basis function approximation. The numerical results indicated that the computational accuracy depended on the radial basis function and the reciprocal multi-quadric function was be...