For the unit sphere embedded in a Euclidean space, we obtain quadrature formulas that are exact for spherical harmonics of a fixed order, have nonnegative weights, and are based on function values at scattered points (sites). The number of scattered sites required is comparable to the dimension of the space for which the quadrature formula is required to be exact. As a part of the proof, we der...

In this paper we solve the problem about optimal interval quadrature formula for the class WrF of differentiable periodic functions with rearrangement invariant set F of their derivatives of order r. We prove that the formula with equal coefficients and n node intervals having equidistant midpoints is optimal for considering classes. To this end a sharp inequality for antiderivatives of rearran...

Similar as in the classical case of polynomials, as is known, paraorthogonal rational functions on the unit circle can be used to obtain quadrature formulas of Szegő-type to approximate some integrals. In the present paper we carry out a thorough discussion of the existence of such rational functions in terms of the underlying Borel measure on the unit circle

Szegö quadrature formulas represent the analogue on the unit circle of the well-known Gauss–Christoffel quadratures for intervals of the real line. In the present work, Szegö formulas are revised and an application to the computation of the Fourier transform given. 2006 Elsevier Inc. All rights reserved.

In this paper we investigate the Szegő-Radau and Szegő-Lobatto quadrature formulas on the unit circle. These are (n + m)-point formulas for which m nodes are fixed in advance, with m = 1 and m = 2 respectively, and which have a maximal domain of validity in the space of Laurent polynomials. That means that the free parameters (free nodes and positive weights) are chosen such that the quadrature...

Our paper reviews Kallay’s results on a geometric version of the classic Newton-Raphson method, in the context of plane curve queries, e.g. curve-curve intersection, point-curve distance computation. Variants of the geometric Newton-Raphson methods are proposed and empirically verified.

It is well known [28] that a number of important classes of univalent functions (e.g. convex, starlike) are related through their derivatives by functions with positive real part. These functions play an important part in problem from signal theory, in moment problems and in constructing quadrature formulas, see Ronning [97] and the references cited therein for some recent applications. In this...

In this paper, two formulas were chosen among those that estimate the suspendedsediment discharge in rivers. These two formulas were Lane and Kalinske and Bagnold. Forstudying and knowing the correlation between input parameters and calculated suspendedsediment discharge (CSSD), the SPSS17 software was used. Input parameters in these twoformulas were as: water velocity, water discharge, suspend...

objective: the two most frequent hypochromic microcytic anemias are β- thalassemia minor (btm) and iron deficiency anemia (ida). several discrimination indices have been proposed to quickly discriminate these similar entities via parameters obtained from automated blood count analyzers. the aim of this study to evaluate the diagnostic reliability of ten discrimination indices in the differentia...

We provide an algorithm to compute the nodes and weights for Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary real poles outside [−1, 1]. Contrary to existing rational quadrature formulas, the computational effort is very low, even for extremely high degrees, and under certain conditions on the poles it can be shown that the complexity is of...