The solution of the radiation transfer equation for the Earth's atmosphere needs to account for the re ectivity of the ground. When using the spherical harmonics method, the solution for this term involves an integral with a particular measure that presents numerical challenges. We are interested in computing a high order Gauss quadrature rule for this measure. We show that the two classical al...

This paper introduces GAUSS a system for the automatic selection of quadrature routines in numerical computation. Given a problem in numerical integration and constraints on time and accuracy, GAUSS comes up with an efficient algorithm to solve it. It banks on a performance database of various algorithms and test problems, an automatic feature identification module and a knowledge methodology t...

We apply the results established in [12] to prove some new fractional Leibniz rules involving BV?,p and S?,p functions, following distributional approach adopted previous works [8], [13], [14]. In order achieve our main results, we revise elementary properties of operators involved framework Besov spaces rephraze Kenig–Ponce–Vega Leibniz-type rule context. well-posedness boundary-value problem ...

It is shown that as m tends to infinity, the error in the integration of the Chebyshev polynomial of the first kind, T{im+2)j±2^x), by an /n-point Gauss integration rule approaches (-!> • 2/(4/2 1), / = 0, 1, ■ • • , m 1, and (-!>' • tt/2, / = m, for all J. 1. Knowledge of the errors in the numerical integration of Chebyshev polynomials of the first kind, Tn(x), by given integration rules has p...

orthogonal zero interpolants (ozi) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. ozi’s can be constructed by the 3-term recurrence relation. these interpolants are found useful in the solution of constrained approximation problems and in the structure of gauss-type quadrature rules. we present some theoretical...