The application of widely known blending methods for constructing C1 bivariate functions interpolating scattered data requires the knowledge of the partial derivatives of first order at the vertices of an underlying triangulation. In this paper we consider the method proposed by Nielson that consists in computing estimates of the first order partial derivatives by minimizing an appropriate quadratic functional, characterized by nonnegative tension parameters.The aim of the paper is to analyse some peculiar properties of this functional in order to construct robust and efficient algorithms for determining the above estimates of the derivatives when we are concerned with extremely large data sets.

On a quadratic functional occurring in a bivariate scattered data interpolation problem / Galligani, Emanuele. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE. - ISSN 0430-3202. - STAMPA. - 48:(2002), pp. 99-117. [10.1007/BF02824741]

On a quadratic functional occurring in a bivariate scattered data interpolation problem

GALLIGANI, Emanuele
2002

Abstract

The application of widely known blending methods for constructing C1 bivariate functions interpolating scattered data requires the knowledge of the partial derivatives of first order at the vertices of an underlying triangulation. In this paper we consider the method proposed by Nielson that consists in computing estimates of the first order partial derivatives by minimizing an appropriate quadratic functional, characterized by nonnegative tension parameters.The aim of the paper is to analyse some peculiar properties of this functional in order to construct robust and efficient algorithms for determining the above estimates of the derivatives when we are concerned with extremely large data sets.
2002
48
99
117
On a quadratic functional occurring in a bivariate scattered data interpolation problem / Galligani, Emanuele. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE. - ISSN 0430-3202. - STAMPA. - 48:(2002), pp. 99-117. [10.1007/BF02824741]
Galligani, Emanuele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/612632
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