Optimal Sample Weights for Hemispherical Integral Quadratures

Abscissas and Weights for Gaussian Quadratures of High Order

Gaussian quadrature rules have hitherto been computed up to the case n = 16 with 15 place accuracy [1].1 In the work in the Numerical Analysis Section of the National Bureau of Standards, frequ ent use has been made of the rule n = 16 and even of halving and quartering the interval for increased accuracy . For this reason, it is felt that the constants for rules of higher order will prove to be...

High-Order Quadratures for Integral Operators with Singular Kernels

A numerical integration method that has rapid convergence for integrands with known singularities is presented. Based on endpoint corrections to the trapezoidal rule, the quadratures are suited for the discretization of a variety of integral equations encountered in mathematical physics. The quadratures are based on a technique introduced by Rokhlin (Computers Math. Applic. 20, pp. 51-62, 1990)...

Methods for Extreme Weights in Sample Surveys Methods for Extreme Weights in Sample Surveys

In survey sampling practice, planned and unplanned variation in the sampling weights can result in inflated sampling variances. As a result, extreme sampling weights are sometimes trimmed to reduce the sampling variance. However, when sampling weights are trimmed, a bias can be introduced into the survey estimates. The goal of sampling weight trimming is to reduce the sampling variance while av...

Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators

Quadratures of Pontryagin Extremals for Optimal Control Problems

We obtain a method to compute effective first integrals by combining Noether’s principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrability by quadratures of optimal control problems with controls taking values on open sets is obtained. We illustrate our approach on some problems taken from the literature. An alternative proof of the integrability of ...