The quasi – interpolant as a tool in elementary polynomial spline theory

  title={The quasi – interpolant as a tool in elementary polynomial spline theory},
  author={Carl de Boor},
and b := sup i ti. For i ∈ ZZ, the i B–spline of order k with (or, for the) knot sequence t is given by the rule Nik(t) := gk(ti, . . . , ti+k; t) (ti+k − ti) gk(s; t) := (s − t) k−1 + taking, for each fixed t, the k divided difference of g(s) := gk(s; t) at ti, . . . ti+k in the usual manner even when some or all of the tj ’s coincide. I leave unresolved any possible ambiguity when t = tj for some j, and concern myself only with left and right limits at such a point; i.e., I replace each t… CONTINUE READING


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On H–extension of functions and spline interpolation”, MRC, U.Wisconsin-Madison. This paper exists only as a reference in other papers, e.g., in [I

  • M. Golomb, I. J. Schoenberg
  • AMS 153,
  • 1968
Highly Influential
8 Excerpts

On Pólya frequency functions IV: the fundamental spline functions and their limits

  • H. B. Curry, I. J. Schoenberg
  • J. Analyse Math
  • 1966
Highly Influential
8 Excerpts

Spline approximation by quasi-interpolants

  • C. de Boor, G. J. Fix
  • J. Approx. Theory
  • 1973
2 Excerpts

Cardinal interpolation and spline functions: II. Interpolation of data of power growth

  • I. J. Schoenberg
  • J. Approx. Theory 6,
  • 1972
2 Excerpts

On the convergence of odd-degree spline interpolation

  • C. de Boor
  • J. Approx. Theory 1,
  • 1968
2 Excerpts

Fix ( 1973 ) , “ Spline approximation by quasi - interpolants ”

  • I. J. Schoenberg
  • J . Approx . Theory
  • 1966
1 Excerpt

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