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EfficientL 2 approximation by splines (1979)

Barrow, D. L. ; Smith, P. W.

Springer

Numerische Mathematik 33 (1979), S. 101-114

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Details

ISSN: 0945-3245

Schlagwort(e): primary 41 A 15 ; secondary 41 A 50

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract LetS N k (t) be the linear space ofk-th order splines on [0, 1] having the simple knotst i determined from a fixed functiont by the rulet i=t(i/N). In this paper we introduce sequences of operators {Q N } N ∞ =1 fromC k [0, 1] toS N k (t) which are computationally simple and which, asN→∞, give essentially the best possible approximations tof and its firstk−1 derivatives, in the norm ofL 2[0, 1]. Precisely, we show thatN k−1(‖(f−Q N f) i ‖−dist2(f (1),S N k−1 (t)))→0 fori=0, 1, ...,k−1. Several numerical examples are given.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01396498

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