Abstract
While the least-squares line and plane problems were formulated such that the unknown parameters could be determined from linear equations, other geometries present more complex non-linear forms. We describe three iterative algorithms in this chapter – the Steepest-descent, the Gauss-Newton and the Levenberg-Marquardt algorithm that can be used for non-linear geometries. We describe these algorithms in the context of the best-fit circle. We formulate the best-fit circle problem and then proceed to solve for its parameters using each of the three algorithms mentioned above.
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References
Forbes, A.B. 1989, Least-Squares Best-Fit Geometric Elements, NPL Report DITC 140/89, National Physical Laboratory. Teddington, UK.
Rao, S. 1996, Engineering Optimization: Theory and Practice, 3rd edn, Wiley-Interscience. New York, NY, USA.
Reklaitis, G.V., Ravindran, A. and Ragsdell, K.M. 1983, Engineering Optimization: Methods and Applications, 1st edn, Wiley-Interscience. New York, NY, USA.
Shakarji, C. 1998, ‘Least-squares fitting algorithms of the NIST Algorithm Testing System’, Journal of Research of the NIST, vol. 103, no. 6, pp. 633–641.
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© 2009 Springer London
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(2009). Non-linear Least-Squares I: Introduction. In: Computational Surface and Roundness Metrology. Springer, London. https://doi.org/10.1007/978-1-84800-297-5_16
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DOI: https://doi.org/10.1007/978-1-84800-297-5_16
Publisher Name: Springer, London
Print ISBN: 978-1-84800-296-8
Online ISBN: 978-1-84800-297-5
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