beliakov-monsplines-2000.pdf (145.67 kB)
Shape preserving approximation using least squares splines
Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.
History
Journal
Analysis in theory and applicationsVolume
16Issue
4Pagination
80 - 98Publisher
Editorial Board of Analysis in Theory and Applications, Kluwer Academic PublishersLocation
Dordrecht, The NetherlandsPublisher DOI
ISSN
1672-4070eISSN
1573-8175Language
engNotes
The original publication can be found at www.springerlink.comPublication classification
C1.1 Refereed article in a scholarly journal; C Journal articleCopyright notice
2000, SpringerUsage metrics
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