Abstract
Motivated by problems of shape preserving tensor product interpolation, tensor products of convex cones in finite dimensional linear spaces are studied in this paper. We recall the notions of projective and injective tensor product cones and derive some of their properties. It is shown that the cones usually considered in shape preserving tensor product interpolation can be represented as intersections of injective tensor product cones. Consequently, sufficient conditions for the fulfillment of the shape constraints are easily derived from corresponding conditions in the univariate case.
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Mulansky, B. (1997). Tensor Products of Convex Cones. In: Nürnberger, G., Schmidt, J.W., Walz, G. (eds) Multivariate Approximation and Splines. ISNM International Series of Numerical Mathematics, vol 125. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8871-4_14
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DOI: https://doi.org/10.1007/978-3-0348-8871-4_14
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9808-9
Online ISBN: 978-3-0348-8871-4
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