Title: APPROXIMATION BY SMOOTH MULTIVARIATE SPLINES ON NON-UNIFORM GRIDS
Abstract: This chapter describes approximation bysmooth multivariate splines on nonuniform grids. It constructs smooth multivariate splines with respect to certain nonuniform grid configurations and establishes local error estimates. The chapter discusses the approximation by smooth piecewise polynomials of several variables. Construction of arbitrary spatial dimension and any degree spline spaces of possibly high global smoothness while preserving the local nature of these spline spaces is still a delicate problem. Error bounds for the approximation by smooth multivariate splines involve typically only a globally maximal mesh size parameter. This does not provide satisfactory information when dealing with highly varying mesh sizes that are a reasonable method to adapt singularities.
Publication Year: 1980
Publication Date: 1980-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 5
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