Scattered data interpolation based upon generalized minimum norm networks

Helmut Pottmann

doi:10.1007/BF01888156

Scattered data interpolation based upon generalized minimum norm networks

Helmut Pottmann^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

A generalization of G. M. Nielson's method for bivariate scattered data interpolation based upon a minimum norm network is presented. The essential part of the new method is the use of a variational principle for definition of function values as well as cross-boundary derivatives over the edges of a triangulation of the data points. We mainly discuss the case of C² interpolants and present some examples including quality control with systems of isophotes.

Original language	English (US)
Pages (from-to)	247-256
Number of pages	10
Journal	Constructive Approximation
Volume	7
Issue number	1
DOIs	https://doi.org/10.1007/BF01888156
State	Published - Dec 1991
Externally published	Yes

Keywords

AMS classification: Primary 65D05, Secondary 41A15
Minimum norm
Multivariate approximation
Scattered data interpolation
Surface fitting

ASJC Scopus subject areas

Analysis
General Mathematics
Computational Mathematics

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10.1007/BF01888156

Cite this

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title = "Scattered data interpolation based upon generalized minimum norm networks",

abstract = "A generalization of G. M. Nielson's method for bivariate scattered data interpolation based upon a minimum norm network is presented. The essential part of the new method is the use of a variational principle for definition of function values as well as cross-boundary derivatives over the edges of a triangulation of the data points. We mainly discuss the case of C2 interpolants and present some examples including quality control with systems of isophotes.",

keywords = "AMS classification: Primary 65D05, Secondary 41A15, Minimum norm, Multivariate approximation, Scattered data interpolation, Surface fitting",

author = "Helmut Pottmann",

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PY - 1991/12

Y1 - 1991/12

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AB - A generalization of G. M. Nielson's method for bivariate scattered data interpolation based upon a minimum norm network is presented. The essential part of the new method is the use of a variational principle for definition of function values as well as cross-boundary derivatives over the edges of a triangulation of the data points. We mainly discuss the case of C2 interpolants and present some examples including quality control with systems of isophotes.

KW - AMS classification: Primary 65D05, Secondary 41A15

KW - Minimum norm

KW - Multivariate approximation

KW - Scattered data interpolation

KW - Surface fitting

UR - http://www.scopus.com/inward/record.url?scp=0043124767&partnerID=8YFLogxK

U2 - 10.1007/BF01888156

DO - 10.1007/BF01888156

M3 - Article

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SP - 247

EP - 256

JO - Constructive Approximation

JF - Constructive Approximation

IS - 1

ER -

Scattered data interpolation based upon generalized minimum norm networks

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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