Adaptive Interpolation by Scaled Multiquadrics

Authors: Bozzini M.¹; Lenarduzzi L.²; Schaback R.³

Source: Advances in Computational Mathematics, Volume 16, Number 4, May 2002 , pp. 375-387(13)

Publisher: Springer

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Abstract:

We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.

Keywords: conditionally positive definite radial basis funct; shape parameters; scaling; solvability

Language: English

Document Type: Regular paper

Affiliations: 1: Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via Bicocca degli Arcimboldi 8, 20126 Milano, Italy E-mail: bozzini@matapp.unimib.it 2: IAMI CNR, via Ampère 56, 20131 Milano, Italy E-mail: licia@iami.mi.cnr.it 3: Universität Göttingen, Lotzerstr. 16-18, D-37083 Göttingen, Germany E-mail: schaback@math.uni-goettingen.de

Publication date: 2002-05-01