# 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.

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