# A comparative analysis of local cubic splines

A comparative analysis of local cubic splines 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational and Applied Mathematics Springer Journals

# A comparative analysis of local cubic splines

, Volume OnlineFirst – May 28, 2018
11 pages

/lp/springer_journal/a-comparative-analysis-of-local-cubic-splines-9SJIJu36Xm
Publisher
Springer International Publishing
Subject
Mathematics; Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical Applications in the Physical Sciences; Mathematical Applications in Computer Science
ISSN
0101-8205
eISSN
1807-0302
D.O.I.
10.1007/s40314-018-0651-1
Publisher site
See Article on Publisher Site

### Abstract

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

### Journal

Computational and Applied MathematicsSpringer Journals

Published: May 28, 2018

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