Hyperspheres and hyperplanes fitted seamlessly by algebraic constrained total least-squares (Q5943025)
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scientific article; zbMATH DE number 1642113
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hyperspheres and hyperplanes fitted seamlessly by algebraic constrained total least-squares |
scientific article; zbMATH DE number 1642113 |
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Hyperspheres and hyperplanes fitted seamlessly by algebraic constrained total least-squares (English)
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28 July 2003
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An algorithm is presented which for each finite set of points in an Euclidean space of any dimension determines all the best fitting circles or lines, spheres or planes, or hyperspheres or hyperplanes. Affine submanifolds are not singularities of the algorithm. The resulting best fitting manifolds remain invariant under rigid transformations. If the best fitting manifold is affine then it coincides with \textit{G. H. Golub} and \textit{C. F. Van Loan}'s affine manifold of total least squares [SIAM J. Numer. Anal. 17, No.~6, 883-893 (1980; Zbl 0468.65011)].
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fitting
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circles
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hyperspheres
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spheres
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total least squares
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algorithm
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best fitting manifold
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