Abstract
For discrete nonlinear least-squares approximation problems ∑ m j=1 f 2 j (x) → min for m smooth functions f j : ℝn → ℝ, a numerical method is proposed which first minimizes each f j separately, and then applies a penalty strategy to gradually force the different minimizers to coalesce. Though the auxiliary nonlinear least-squares method works on ℝn·m, it is shown that the additional computational requirements consist of m − 1 gradient evaluations plus O(m · n) operations. The application to discrete rational approximation is discussed, and numerical examples are given.
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Dedicated to the memory of Lothar Collatz
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© 1992 Springer Basel AG
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Schaback, R. (1992). A Multi-Parameter Method for Nonlinear Least-Squares Approximation. In: Braess, D., Schumaker, L.L. (eds) Numerical Methods in Approximation Theory, Vol. 9. ISNM 105: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 105. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8619-2_15
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DOI: https://doi.org/10.1007/978-3-0348-8619-2_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9702-0
Online ISBN: 978-3-0348-8619-2
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