Cardinal Interpolation and Spline Functions VII. the Behavior of Cardinal Spline Interpolants as their Degree Tends to Infinity

  • I. J. Schoenberg
Part of the Contemporary Mathematicians book series (CM)

Abstract

Let F(x) be a function from ℝ to ℂ and let
$$S_m \left( x \right)\, = \,\sum\limits_{ - \infty }^\infty {F\left( \nu \right)L_m \left( {x - \nu } \right)}$$
(1)
be the spline function of degree 2m−1, with knots at the integers, that interpolates F(x) at all the integers. We know that S m (x), as defined by (1), exists if F(x) grows at most like a power | x |γ as x → ± ∞ (see [7]). Here we investigate conditions which will insure that S m (x) will converge to F(x) as m → ∞.

Keywords

Entire Function Spline Function Power Growth Direct Definition Spline INTERPOLANTS 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • I. J. Schoenberg
    • 1
  1. 1.Mathematics Research Center, University of WisconsinMadisonUSA

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