Geometric fit of a point set by generalized circles

Publication: Research - peer-reviewJournal article – Annual report year: 2010

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In our paper we approximate a set of given points by a general circle. More precisely, given two norms k 1 and k 2 and a set of points in the plane, we consider the problem of locating and scaling the unit circle of norm k 1 such that the sum of weighted distances between the circumference of the circle and the given points is minimized, where the distance is measured by a norm k 2. We present results for the general case. In the case that k 1 and k 2 are both polyhedral norms, we are able to solve the problem by investigating a finite candidate set.
Original languageEnglish
JournalJournal of Global Optimization
Publication date2010
Volume51
Issue1
Pages115-132
ISSN0925-5001
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 2

Keywords

  • circle location, dimensional facility, minisum, polyhedral norms
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