PORTUGALIAE MATHEMATICA Vol. 53, No. 3, pp. 355366 (1996) 

Spline Approximation and Generalized Turán QuadraturesMilan A. Kova\v cevi\'c and Gradimir V. Milovanovi\'cFaculty of Electronic Engineering, Department of Mathematics,P.O. Box 73, 18000 Ni\v s  YUGOSLAVIA Email: grade\@efnis.elfak.ni.ac.yu Abstract: In this paper, which is connected with our previous work [16], we consider the problem of approximating a function $f$ on the halfline by a spline function of degree $m$ with $n$ (variable) knots (multiplicities of the knots are greater or equal than one). In the approximation procedure we use the moments of the function $r\mapsto f(r)$ and its derivatives at the origin $r=0$. If the approximation exists, we show that it can be represented in terms of the generalized Turán quadrature relative to a measure depending on $f$. Also the error in the spline approximation formula is expressed by the error term in the corresponding quadrature formula. A numerical example is included. Keywords: Spline approximation; Turán quadratures; $s$orthogonal polynomials. Classification (MSC2000): 41A15, 65D32; 33C45 Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1996 Sociedade Portuguesa de Matemática
