Comp. Appl. Math. https://doi.org/10.1007/s40314-018-0651-1 1 2 T. Zhanlav · R. Mijiddorj Received: 29 September 2016 / Revised: 23 May 2017 / Accepted: 15 May 2018 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018 Abstract In this note, we develop a local construction of cubic splines and make a com- parative analysis of local integro cubic splines. We also derive explicit formulae for a local integro cubic spline and its ﬁrst two derivatives. These formulae are short and four-point ones that require less computational cost compared to an integro cubic spline quasi-interpolant. Keywords Cubic splines · Approximation properties · End conditions Mathematics Subject Classiﬁcation 65D05 · 65D07 1 Introduction In last years, the local construction of splines has attracted a lot of attention from researchers. For example, the local integro cubic spline was constructed in Zhanlav and Mijiddorj (2010). Quite recently, the integro cubic spline quasi-interpolant was developed in Boujraf et al. (2015) and some comparisons were made with the results obtained in Zhanlav and Mijiddorj (2010). As seen from Boujraf et al. (2015) and Zhanlav and Mijiddorj (2010), the approxi- mation order of these two integro splines is equal and is O(h ). The difference between
Computational and Applied Mathematics – Springer Journals
Published: May 28, 2018
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