Abstract
In this paper a special class of one-dimensional L-splines of order 4 is studied, which naturally appear in the computation of interpolation and smoothing with multivariate polysplines. Fast algorithms are provided for interpolation and smoothing with this class of L-splines, as well as a generalization of the Reinsch algorithm to this setting. The explicit description of all mathematical expressions permits a simple and direct numerical implementation. Applications are provided to financial data of the index S&P500, for the fast calculation of statistically interesting quantities, as cross validation (scores), generalized cross validation (scores) for finding the best smoothing parameter \(\alpha \), and the residual sum of squares.
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Notes
Data downloaded via https://finance.yahoo.com website. From all S&P500 prices we have subtracted the value 2500 to avoid working with big numbers.
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Communicated by Tom Lyche.
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O. Kounchev was partially supported by the Alexander von Humboldt Foundation, Bonn, while all were supported by Grant DN-02-13 and Grant KP-06-H32-8 with Bulgarian NSF.
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Kounchev, O., Render, H. & Tsachev, T. On a class of L-splines of order 4: fast algorithms for interpolation and smoothing. Bit Numer Math 60, 879–899 (2020). https://doi.org/10.1007/s10543-020-00801-8
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DOI: https://doi.org/10.1007/s10543-020-00801-8