Near-interpolation |
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Authors: | Scott N Kersey |
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Institution: | (1) Department of Mathematics, Case Western Reserve University, USA; e-mail: snk@po.cwru.edu, US |
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Abstract: | Summary. A parametric curve fL
2
(m)
(a,b]ℝ
d
) is a ``near-interpolant' to prescribed data z
ij
ℝ
d
at data sites t
i
a,b] within tolerances 0<ɛ
ij
≤∞ if |f
(j−1)
(t
i
)−z
ij
|≤ɛ
ij
for i=1:n and j=1:m, and a ``best near-interpolant' if it also minimizes ∫
a
b
|f
(m)
|2. In this paper optimality conditions are derived for these best near-interpolants. Based on these conditions it is shown
that the near-interpolants are actually smoothing splines with weights that appear as Lagrange multipliers corresponding to
the constraints. The optimality conditions are applied to the computation of near-interpolants in the last sections of the
paper.
Received September 4, 2001 / Revised version received July 22, 2002 /
Published online October 29, 2002
Mathematics Subject Classification (1991): 41A05, 41A15, 41A29 |
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Keywords: | |
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