Let N be a positive integer and x(j) be N equidistant points. We propose an algorithmic approach for approximate calculation of sums of the form Sigma(N)(j=1) F(x(j)). The method is based on the Gaussian type quadrature ...

We calculate the probability that a k-homogeneous polynomial in n variables attain a local maximum on a vertex in terms of the “sharpness” of the vertex, and then study the dependence of this measure on the growth of ...

In the present work, our goal is to establish a study of some families of quadratic polynomial vector fields connected to orthogonal polynomials that relate, via two different points of view, the qualitative and the algebraic ...

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained ...

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained ...

The present paper is a continuation of a recent article [SIAM T. Numer. Anal., 52 (2014), pp. 1867-1886], where we proposed an algorithmic approach for approximate calculation of sums of the form Sigma(N)(j=1) f (j). The ...