Spline Interpolation and Fitting in $$\mathbb {R}^{n}$$ R n

Ines Adouani and Chafik Samir ()
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Ines Adouani: University of Sousse, Higher Institute of Applied Sciences and Technology of Sousse (ISSAT)
Chafik Samir: University of Clermont Auvergne (UCA)

Chapter Chapter 2 in Regression and Fitting on Manifold-valued Data, 2024, pp 9-26 from Springer

Abstract: Abstract This chapter unfolds a comprehensive exploration of the fitting and interpolation problem in $$\mathbb {R}^{n}$$ R n . We present a formal definition of the fitting problem, simultaneously addressing the core challenge of accurately interpolating time-labeled data in Euclidean space. Subsequently, a thorough review of key definitions related to Bézier splines ensues, highlighting the prerequisites for achieving $$C^{m}$$ C m continuity, ( $$m=0,1,2$$ m = 0 , 1 , 2 ). The chapter culminates in the introduction of an innovative method for solving the interpolation problem in $$\mathbb {R}^{n}$$ R n through the use of $$C^{m}$$ C m Bézier splines. This approach adeptly navigates the complexities of fitting data in multiple dimensions, ensuring the desired continuity up to the mth order and providing a nuanced and effective solution to this intricate problem.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-61712-6_2

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DOI: 10.1007/978-3-031-61712-6_2

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