A nonlinear algorithm for monotone piecewise bicubic interpolation

• We present an algorithm for monotone interpolation on a rectangular mesh.
• We use the sufficient conditions for monotonicity of Carlton and Fritsch.
• We use nonlinear techniques to approximate the partial derivatives at the grid points.
• We develop piecewise bicubic Hermite interpolants with these approximations.
• We present some numerical examples where we compare different results.

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 Aràndiga (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.