Locally tensor product functions
type: Item
instance of: scholarly article
title: Locally tensor product functions
zbMATH Open document ID: 1116.41015
author: Christophe Rabut
published in: Numerical Algorithms
publication date: 2005-05-20T00:00:00Z
review text: A class of tensor product functions in subdomains (usually with different ``steps'' of the grid for different subdomains) is constructed. The global function is not a tensor product function. Some fine error bounds for these functions are unknown. The property of smoothness and some discontinuities of global functions are not investigated. These functions cumulate main advantages of tensor product functions and the possibility of numerous (dense grid) degrees of freedom in some parts of the space, while less (coarse grid) degrees of freedom in other parts. This allows the user to have a fine grid in some regions, a coarse grid in other regions without any interaction between these two grids. The cubic B-splines are used in the space of two dimensions, because a cubic space spline has more knots than the dimension of the space (``knot''- a junction between two different polynomials). The choice of the knots of the B-splines is something strategic. The form and the properties of the constructed functions depend on it. If the underlying process presents some irregularity in an isolated point, centres of the B-splines can be concentrated around this point, and the levels of the B-splines will be greater there. Approximation of functions, or data, with such functions gives satisfactory results, as shown by numerical experimentation.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D15
zbMATH DE Number: 2170146
zbMATH Keywords: tensor product function
zbMATH Keywords: B-splines
zbMATH Keywords: subdomains
zbMATH Keywords: local refinement
reviewed by: V. L. Leontiev
MaRDI profile type: Publication
full work available at URL: s11075-004-3646-5
OpenAlex ID: W1996434074
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cites work: Q4438266
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DOI: 10.1007/S11075-004-3646-5
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description: scientific article; zbMATH DE number 2170146