%0 Journal Article
%T Bound-preserving interpolation using quadratic splines
%J Journal of Mathematical Modeling
%I University of Guilan
%Z 2345-394X
%A Saeidian, Jamshid
%A Sarfraz, Muhammad
%A Jalilian, Sajad
%D 2022
%\ 09/01/2022
%V 10
%N 3
%P 407-419
%! Bound-preserving interpolation using quadratic splines
%K Shape preserving interpolation
%K Boundedness
%K quadratic splines
%K Linear programming
%R 10.22124/jmm.2021.19496.1676
%X 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.
%U https://jmm.guilan.ac.ir/article_5323_ed3559e2689004ef7a3feacb3ed4679e.pdf