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RESEARCH PRODUCT

A nonlinear algorithm for monotone piecewise bicubic interpolation

Francesc Aràndiga

subject

Hermite polynomialsApplied MathematicsMathematical analysisMonotone cubic interpolationStairstep interpolation010103 numerical & computational mathematics02 engineering and technology01 natural sciencesComputational MathematicsComputer Science::GraphicsMonotone polygon0202 electrical engineering electronic engineering information engineeringPiecewisePartial derivativeBicubic interpolation020201 artificial intelligence & image processing0101 mathematicsMathematicsInterpolation

description

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 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.

yearjournalcountryeditionlanguage
2016-01-01Applied Mathematics and Computation
https://doi.org/10.1016/j.amc.2015.08.027