Algorithm to construct integro splines

Renchin-Ochir Mijiddorj; Tugal  Zhanlav

doi:10.21914/anziamj.v63.15855

Authors

Renchin-Ochir Mijiddorj Mongolian National University of Education https://orcid.org/0000-0002-4845-9019
Tugal Zhanlav Mongolian Academy of Sciences https://orcid.org/0000-0003-0743-5587

DOI:

https://doi.org/10.21914/anziamj.v63.15855

Keywords:

super-convergence, numerical integration, differentiation and integration operations, polynomial and nonpolynomial, histospline

Abstract

We study some properties of integro splines. Using these properties, we design an algorithm to construct splines \(S_{m+1}(x)\) of neighbouring degrees to the given spline \(S_{m}(x)\) with degree \(m\). A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs.

doi:10.1017/S1446181121000316

Author Biographies

Renchin-Ochir Mijiddorj, Mongolian National University of Education

Department of Informatics, Mongolian National University of Education, Ulaanbaatar, Mongolia.

Tugal Zhanlav, Mongolian Academy of Sciences

Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia.