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Moment-preserving spline approximation and Turán quadratures. (English) Zbl 0659.65010
Numerical mathematics, Proc. Int. Conf., Singapore 1988, ISNM, Int. Ser. Numer. Math. 86, 357-365 (1988).
Authors’ summary: [For the entire collection see Zbl 0644.00018.]
We consider the problem of approximating a function f of the radial distance r in $${\mathbb{R}}^ d$$ on $$0\leq r<\infty$$ by a spline function of degree m and defect k, with n (variable) knots, matching as many of the initial moments of f as possible. We analyse the case when the defect k is an odd integer, especially when $$k=3$$. We show that, if the approximation exists, it can be represented in terms of generalized Turán quadrature relative to a measure depending on f. The knots of the spline are the zeros of the corresponding s-orthogonal polynomials (s$$\geq 1)$$. Numerical example is included.
Reviewer: J.N.Lyness

##### MSC:
 65D15 Algorithms for approximation of functions 65D07 Numerical computation using splines 41A15 Spline approximation