Titlebook: Numerical Integration IV; Proceedings of the C H. Brass,G. Hämmerlin Conference proceedings 1993 Springer Basel AG 1993 integration.Mathema

SPASM

Multivariate Boolean Midpoint Rules,with lattice rules of multivariate numerical integration (Sloan 1985, 1987). In this paper we will construct Boolean midpoint rules for multivariate numerical integration of arbitrary dimensions which are based on the ideas of multivariate Boolean interpolation and which extend results of Delvos (19

Headstrong

A relation between cubature formulae of trigonometric degree and lattice rules,ndition for the weights, we show that such formulae can be approached with the tools used to construct cubature formulae of algebraic degree. We also approach them from the field of lattice rules. A new family of cubature formulae of trigonometric degree with the lowest possible number of points is

MAIM

Distribution of Points in Convergent Sequences of Interpolatory Integration Rules: The Rates,eview previous results, which show that . the points in the rules behave like zeros of appropriate orthogonal polynomials, and half may be arbitrarily distributed. In the case of the interval (-1,1), this usually means that half the points have .. We also present and prove a new result relating the

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Bounds for Peano kernels,e are functional of the form . The error is the functional .. The degree of . is the number deg Q ≔ sup{.: ..] = 0}, where .. denotes the space of polynomials of degree ≤ . . The most interesting quadrature rules are the Gaussian rules (math), which are characterized as rules with . evaluation point

Ambiguous

florid

–吃

,Variance in Quadrature — a Survey,small variance and high algebraic degree was first considered by Chebyshev in 1874. Since that time, several investigations on this subject can be found in literature. The purpose of this paper is to give a survey of the results and open problems in this field.

Redundant

Gauss-type Quadrature Rules for Rational Functions, question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as to match the most important poles of the integrand. We describe two methods for generating such quadrature rules numerically and report on computational experie

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Quadrature rules derived from linear convergence accelerations schemes,do this we first approximate the integral with a trapezoidal sum, then apply a linear convergence acceleration scheme to approximate this infinite sum with a linear combination of a finite number of terms. We will study two important cases in detail, namely when the integrand is oscillating or decay

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