Abstract
For fitting curves or surfaces to observed or measured data, a common criterion is orthogonal distance regression. We consider here a natural generalization of a particular formulation of that problem which involves the replacement of least squares by the Chebyshev norm. For example, this criterion may be a more appropriate one in the context of accept/reject decisions for manufactured parts. The resulting problem has some interesting features: it has much structure which can be exploited, but generally the solution is not unique. We consider a method of Gauss-Newton type and show that if the non-uniqueness is resolved in a way which is consistent with a particular way of exploiting the structure in the linear subproblem, this can not only allow the method to be properly defined, but can permit a second order rate of convergence. Numerical examples are given to illustrate this.
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65D10, 65K05
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Al-Subaihi, I., Watson, G. Fitting Parametric Curves and Surfaces by l∞ Distance Regression. Bit Numer Math 45, 443–461 (2005). https://doi.org/10.1007/s10543-005-0018-z
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DOI: https://doi.org/10.1007/s10543-005-0018-z