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An approach to nonlinear l 1 data fitting

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Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((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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  2. Coleman, T.F. and Conn, A.R. Second-order conditions for an exact penalty function. Math. Prog. 19 (1980) 178–185.

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  3. Coleman, T.F. and Conn, A.R. Nonlinear programming via an exact penalty function: global analysis. Math. Prog. to appear.

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  4. Colman, T.F. and Conn, A.R. Nonlinear programming via an exact penalty function: asymptotic analysis. Math. Prog. to appear.

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  5. El-Attar, R.A.; Vidyasagar, M. and Dutta, S.R.K. An Algorithm for l 1-norm minimization with application to nonlinear l 1-approximation. SIAM J. Num. Anal. 16 (1979) 70–86.

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  6. Overton, M.L. and Murray, W. A Projected Lagrangian algorithm for nonlinear l 1 optimization. SIAM J. Sci. and Stat. Comp. to appear.

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Authors and Affiliations

  1. Computer Science Department, The University of Waterloo, Waterloo, Canada

    Richard H. Bartels & Andrew R. Conn

Authors
  1. Richard H. Bartels
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  2. Andrew R. Conn
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Editor information

J. P. Hennart

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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

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