Titlebook: Numerical Integration III; Proceedings of the C H. Braß,G. Hämmerlin Conference proceedings 1988 Springer Basel AG 1988 integration.mathema

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What is a Good Quadrature Error Estimate ?,Automatic quadrature packages that undertake to achieve a specified accuracy typically have the following ingredients [RICE]:

genuine

Monosplines and Moment Preserving Spline Approximation,We discuss the problem of choosing the knots of a spline approximation to a given function so as to match a maximal number of moment conditions.

Connotation

吹牛需要艺术

Universal quadrature rules in the space of periodic functions, mostly we are interested in rules, which work well for many classes of functions. It is the aim of this paper to make this idea more precise by the definition and discussion of “universal (quadrature) rules”.

冷漠

Gaussian Quadrature Formulae Involving Derivatives of Lacunary Type,e pairs by an incidence matrix .where .. = 1 if (.) ∈ ., and .. = 0 otherwise. If the knots .. and the weights .. are chosen so that the formula will be exact for polynomials of utmost degree, we call the formula to be of ..

Commonplace

Jacobi Moments and a Family of Special Orthogonal Polynomials,s .since the recurrence relation for the .may be derived via modified moments (e.g. Chebyshev moments) using a Cholesky type process. Moreover, Gauß-type formulas can be constructed numerically from the recurrence relation.

abracadabra

Some Comments on Quadrature Rule Construction Criteria,opics include algebraic and trigonometric degree, Romberg Integration, and the criteria for “Good Lattice” rules. This paper is solely concerned with solidifying known theory. No new results are given here.

闪光东本

容易懂得

圆锥体

Asymptotic Behaviour of Peanokernels of Fixed Order,ting of all functions with an . − 1th absolutely continuous derivative. If .. is exact for polynomials of degree . − 1, the error can be estimated for every . ∈ .. [−1, 1] by using the . th Peano kernel: . (cf. Braß [1], p.39). We therefore have the unimprovable bounds . and