Discrete Approximation by First-Degree Splines with Free Knots
DOI:
https://doi.org/10.53555/ms.v4i5.621Keywords:
splines of degree one, splines with free knots, best approximation, discrete approx- imation, Lp-approximation (1 ≤ p ≤ ∞), existence theorem, first-degree splines, broken linesAbstract
This paper deals with the approximation of discrete real-valued functions by first-degree splines (broken lines) with free knots for arbitrary Lp-norms (1 ≤ p ≤ ∞). We prove the existence of best approximations und derive statements on the position of the (free) knots of a best approximation. Building on this, elsewhere we develop an algorithm to determine a (global) best approximation in the L2-norm.
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References
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