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An approach to nonlinear l 1 data fitting

Part of the Lecture Notes in Mathematics book series (LNM,volume 909)

Abstract

The traditional method of data fitting is by the least squares (l 2) technique. When the data is good—reasonably accurate with normally distributed errors—this method is ideal. When the data is bad—contaminated by occasional wild values—then the l 1 technique (minimizing sums of absolute values of residuals) has much to recommend it. This paper surveys the strategy of a globally and superlinearly convergent algorithm to minimize sums of absolute values of C 2 functions. The approach to be presented is closely related to the use of a certain, piecewise differentiable penalty function to solve nonlinear programming problems.

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Bibliography

  1. Bartels, R.H. and Conn, A.R. Linearly constrained discrete l 1 problems. ACM Trans. on Math. Software 6 (1980) 594–608.

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© 1982 Springer-Verlag

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Bartels, R.H., Conn, A.R. (1982). An approach to nonlinear l 1 data fitting. In: Hennart, J.P. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092959

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  • DOI: https://doi.org/10.1007/BFb0092959

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11193-1

  • Online ISBN: 978-3-540-38986-6

  • eBook Packages: Springer Book Archive