Displaying similar documents to “Spline quasi-interpolants and quadrature formulas.”

Splines in Numerical Integration

Udovičić, Zlatko (2010)

Mathematica Balkanica New Series

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AMS Subj. Classification: 65D07, 65D30. We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coefficients of the polynomials...

Summation of slowly convergent series

Walter Gautschi (1994)

Banach Center Publications

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Among the applications of orthogonal polynomials described briefly on my previous visit to this Center [9, §3.2] were slowly convergent series whose terms could be represented in terms of the Laplace transform at integer arguments. We proposed to sum such series by means of Gaussian quadrature rules applied to suitable integrals involving weight functions of Einstein and Fermi type (cf. [13]). In the meantime it transpired that the technique is applicable to a large class of numerical...

Penalized Least Squares Fitting

von Golitschek, Manfred, Schumaker, Larry (2002)

Serdica Mathematical Journal

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* Supported by the Army Research Office under grant DAAD-19-02-10059. Bounds on the error of certain penalized least squares data fitting methods are derived. In addition to general results in a fairly abstract setting, more detailed results are included for several particularly interesting special cases, including splines in both one and several variables.