Incomplete total least squares (Q1282358)

Total least squares (TLS) are fitting data points with some model function such that the sum of squared orthogonal distances is minimized. The authors 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 one. In this situation an incomplete TLS fit by a finite piece of straight line is introduced and then general model functions with linear parameter are studied. For fitting with them a descent algorithm is adapted. In the last section of the paper incomplete TLS fitting with a segment of a circle, the area of a circle in space, with a cylinder, and with a rectangle are discussed and numerical examples for each case are given.