Incomplete total least squares

Fitting data points with some model function such that the sum of squared o rthogonal 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 s uch that there might be no perpendiculars from certain data points onto the model function and where one has to replace certain orthogonal distances b y shortest ones, e.g. to corner or border line points. We introduce this co nsidering 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/Spath (1997), Spat h (1996), Spath (1997a) and Spath (1997b)) for fitting with them. As applic ations (to be used in computational metrology) we discuss incomplete TLS fi tting with a segment of a circle, the area of a circle in space, with a cyl inder, and with a rectangle (see also Gander/Hrebicek (1993)). Numerical ex amples are given for each case. Mathematics Subject Classification (1991): 65D10.