Incomplete total least squares |
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Authors: | K Brüntjen H Späth |
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Institution: | (1) Paulstrasse 19, D-26129 Oldenburg, Germany , DE;(2) Department of Mathematics, University of Oldenburg, P.O. Box 2503, D-26111 Oldenburg, Germany , DE |
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Abstract: | Fitting data points with some model function such that the sum of squared orthogonal distances is minimized is well-known
as TLS, i.e. as total least squares, see Van Huffel (1997). We consider situations where the model is such that there might
be no perpendiculars from certain data points onto the model function and where one has to replace certain orthogonal distances
by shortest ones, e.g. to corner or border line points. We introduce this considering the (now incomplete) TLS fit by a finite
piece of a straight line. Then we study general model functions with linear parameters and modify a well-known descent algorithm
(see Seufer (1996), Seufer/Sp?th (1997), Sp?th (1996), Sp?th (1997a) and Sp?th (1997b)) for fitting with them. As applications
(to be used in computational metrology) we discuss incomplete TLS fitting with a segment of a circle, the area of a circle
in space, with a cylinder, and with a rectangle (see also Gander/Hrebicek (1993)). Numerical examples are given for each case.
Received August 27, 1997 / Revised version received February 23, 1998 |
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Keywords: | Mathematics Subject Classification (1991):65D10 |
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