Spherical t-designs are point sets XM := {x1, . . . ,xM} ⊂ S2 which provide quadrature rules with equal weights for the sphere which are exact for polynomials up to degree t. In this paper we consider the problem of finding numerical spherical t-designs on the sphere S2 for high polynomial degree t ∈ N. That is, we compute numerically local minimizers of a certain quadrature error At(XM ). The ...

Multiple integrals encountered when evaluating posterior densities in Bayesian estimation were approximated using Multivariate Gaussian Quadrature (MGQ). Experimental results for a linear regression model suggest MGQ provides better approximations to unknown parameters and error variance than simple Monte Carlo based approximations. The authors are Graduate Research Assistant, Professor and Gra...

Geometries for measuring radome characteristics can usually be split into two categories. The first category always has the antenna inside the radome pointing along the range axis. The second category has the antenna maintaining a fixed relationship with respect to the radome during each scan of data. A facility can generally be designed to minimize measurement errors in one of the two geometri...

Workpiece localization has direct relations with many manufacturing automation applications. In order to gain accurate workpiece measurement by coordinate measuring machines (CMM) or on-machine measurement system, the touch trigger probe is widely adopted. In spite of the high repeatability of the touch trigger probe, there are still error sources associated with the probe. In this paper, we wi...

Given a positive bounded Borel measure μ on the interval [−1, 1], we provide convergence results in Lμ2 -norm to a function f of its sequence of rational interpolating functions at the nodes of rational Gauss-type quadrature formulas associated with the measure μ. As an application, we construct rational interpolatory quadrature formulas for complex bounded measures σ on the interval, and give ...

Abstract This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space ( ) 2 (0,1) m L . In this paper the quadrature sum consists of values of the integrand and its first derivative at nodes. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number 1 N m ≥ ...

Product integration methods for Cauchy principal value integrals based on piecewise Lagrangian interpolation are studied. I t is shown that for this class of quadrature methods the truncation error has an asymptotic expansion in integer powers of the step-size, and that a method with an asymptotic expansion in even powers of the step-size does not exist. The relative merits of a quadrature meth...