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

In this article we thoroughly investigate the possibility of employing the exact computation of the free rigid body motion as a component of splitting methods for problems of rigid bodies subject to external forces. We review various matrix and quaternion representations of the solution of the free rigid body equation, which involve Jacobi ellipic functions and elliptic integrals, and are amena...

This paper is devoted to prove the unbounded divergence on superdense sets, with respect to product quadrature formulas of interpolatory type on Jacobi nodes. Mathematics Subject Classification (2010): 41A10, 41A55, 65D32.

Recently, we have extended SDP by adding a quadratic term in the objective function and give a potential reduction algorithm using NT directions. This paper presents a predictor-corrector algorithm using both Dikin-type and Newton centering steps and studies properties of Dikin-type step. In this algorithm, when the condition K(XS) is less than a given number K0, we use Dikin-type step. Otherwi...

The paper introduces several approximate maximum likelihood estimators of the parameters sub-fractional Chan-Karolyi-Longstaff-Sanders (CKLS) interest rate model and obtains their rates convergence. A new algorithm inspired by Newton-Cotes formula is presented to improve accuracy estimation. are useful for simulation rates. proposed could be other stochastic computation. It also proposes a gene...

The goal of Geometric Constraint Solving is to find 2D or 3D placements of some geometric primitives fulfilling some geometric constraints. The common guideline is to solve them by a numerical iterative method (e.g. Newton-Raphson method). A sole solution is obtained whereas many exist. But the number of solutions can be exponential and methods should provide solutions close to a sketch drawn b...

We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by first using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane, then transforming this into a real integral on the finite interval [0, 1], and finally applying a standard quadrature formula to this integral. The method r...