Abstract
We introduce a class of bi- and multivariate cubic L 1 interpolating splines, the coefficients of which are calculated by minimizing the sum of the L 1 norms of second derivatives. The focus is mainly on bivariate cubic L 1 splines for C 1 interpolation of data located at the nodes of a tensor-product grid. These L 1 splines preserve the shape of data even when the data have abrupt changes in magnitude or spacing. Extensions to interpolation of regularly spaced and scattered bi- and multivariate data by cubic and higher-degree surfaces/hypersurfaces on regular and irregular rectangular/quadrilateral/hexahedral and triangular/tetrahedral grids are outlined.
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