In this paper we describe the use of multivariate Chebyshev polynomials in computing spectral derivations and Clenshaw–Curtis type quadratures. The multivariate Chebyshev polynomials give a spectrally accurate approximation of smooth multivariate functions. In particular we investigate polynomials derived from the A2 root system. We provide analytic formulas for the gradient and integral of A2 ...

Moment functions are widely used in image analysis as feature descriptors. Compared to geometric moments, orthogonal moments have become more popular in image analysis for their better representation capabilities. In comparison to continuous orthogonal moments discrete orthogonal moments provide a more accurate description of the image features. This paper compares the performance of discrete o...

We examine two multidimensional optimization problems that are formulated in terms of tropical mathematics. The problems are to minimize nonlinear objective functions, which are defined through the multiplicative conjugate vector transposition on vectors of a finitedimensional semimodule over an idempotent semifield, and subject to boundary constraints. The solution approach is implemented, whi...

In this paper, we are going to solve a class of ordinary differential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the first kind, then we solve the ordinary differential equations by using the Adomian decomposition method

This is the second part in a series of papers on using spectral sparse grid methods for solving higher-dimensional PDEs. We extend the basic idea in the first part [18] for solving PDEs in bounded higher-dimensional domains to unbounded higher-dimensional domains, and apply the new method to solve the electronic Schrödinger equation. By using modified mapped Chebyshev functions as basis functio...