Abstract
In this article, we adress the problem of approximating scattered data points by C 1-smooth polynomial spline curves using L 1-norm optimization. The use of this norm helps us to preserve the shape of the data even near to abrupt changes. We introduced a five-point sliding window process for L 1 spline approximation but this method can be still time consuming despite its linear complexity. Consequently, based on new algebraic results obtained for L 1 approximation on any three points, we define in this article a more efficient method.
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Gajny, L., Nyiri, É., Gibaru, O. (2013). Fast Polynomial Spline Approximation for Large Scattered Data Sets via L 1 Minimization. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_91
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DOI: https://doi.org/10.1007/978-3-642-40020-9_91
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