A nonlinear algorithm for monotone piecewise bicubic interpolation

In this paper we present an algorithm for monotone interpolation of monotone data on a rectangular mesh by piecewise bicubic functions. Carlton and Fritsch (1985) develop conditions on the Hermite derivatives that are sufficient for such a function to be monotone. Here we extend our results of Arandiga (2013) to obtain nonlinear approximations to the first partial and first mixed partial derivatives at the mesh points that allow us to construct a monotone piecewise bicubic interpolants. We analyze its order of approximation and present some numerical experiments. (C) 2015 Elsevier Inc. All rights reserved.