Abstract
For the approximation of gradients from data values at vertices of a uniform grid, we compare two methods based on cubic spline interpolation with a classical method based on finite differences. For univariate cubic splines, we use the so-called de Boor’s Not a Knot property and a new method giving pretty good slopes. Then these methods are used on parallels to the axes for estimating gradients on bivariate grids. They are illustrated by several numerical examples.
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Sablonnière, P. (2009). Gradient Approximation on Uniform Meshes by Finite Differences and Cubic Spline Interpolation. In: Hancock, E.R., Martin, R.R., Sabin, M.A. (eds) Mathematics of Surfaces XIII. Mathematics of Surfaces 2009. Lecture Notes in Computer Science, vol 5654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03596-8_19
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DOI: https://doi.org/10.1007/978-3-642-03596-8_19
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