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Lyche, Tom; Schumaker, Larry L.; Stanley, Sonya

Quasi-interpolants based on trigonometric splines. (English) Zbl 0912.41008

J. Approximation Theory 95, No. 2, 280-309 (1998).
In this paper the authors develop a general theory of quasi-interpolants based on trigonometric splines. Although the analysis is parallel to the familiar treatment of quasi-interpolants based on polynomial splines, the details are complicated because of the nature of trigonometric splines. In addition to developing a general theory they give an detailed treatment of two interesting classes of quasi-interpolants based on derivative formation and on simple point evaluation. The authors provide some general remarks as to how further studies in related fields can be carried on.
Reviewer: G.D.Dikshit (Auckland)

Cited in 24 Documents

MSC:

41A15 Spline approximation
41A30 Approximation by other special function classes

Keywords:

quasi-interpolants; trigonometric B-splines; Marsden identities; extended knot sequence
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\textit{T. Lyche} et al., J. Approx. Theory 95, No. 2, 280--309 (1998; Zbl 0912.41008)
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References:

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