Sunto
L’applicazione di noti metodi che utilizzano funzioni di tipo blending per la costruzione di funzioni bivariate C1 per l’interpolazione di dati, richiede la conoscenza delle derivate parziali del primo ordine ai vertici di una triangolazione sottostante. In questo lavoro consideriamo il metodo proposto da Nielson, che consiste nel calcolare stime delle derivate parziali del primo ordine minimizzando un opportuno funzionale quadratico, caratterizzato da parametri di tensione non negativi. Scopo del lavoro è l’analisi di alcune proprietà particolari di questo funzionale per la costruzione di algoritmi efficienti e robusti per la determinazione delle stime suddette delle derivate quando si ha a che fare con insiemi di dati di grandi dimensioni.
Abstract
The application of widely known blending methods for constructingC 1 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.
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Galligani, E. On a quadratic functional occurring in a bivariate scattered data interpolation problem. Ann. Univ. Ferrara 48, 99–117 (2002). https://doi.org/10.1007/BF02824741
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DOI: https://doi.org/10.1007/BF02824741