Bound-preserving interpolation using quadratic splines

Document Type : Research Article

Authors

1 Faculty of Mathematical Sciences and Computer, Kharazmi University, No. 50, Taleghani Avenue, Tehran, Iran

2 Department of Information Science, College of Life Sciences, Kuwait University, Sabah AlSalem University City, Shadadiya, Kuwait

Abstract

In this work, we study a data visualization problem which is classified in the field of shape-preserving interpolation. When   function  is known to be bounded, then it is  natural to expect its interpolant to adhere boundedness. Two spline-based techniques are proposed to handle this kind of problem. The proposed methods   use quadratic splines as basis and involve solving a linear programming or a mixed integer linear  programming problem which gives $C^1$ interpolants. An energy minimization technique is employed to gain the optimal smooth solution. The reliability  and  applicability of  the proposed techniques  have been illustrated through examples.

Keywords

Journal of Mathematical Modeling
Volume 10, Issue 3
September 2022
Pages 407-419

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