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SENSOP: A derivative-free solver for nonlinear least squares with sensitivity scaling

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Abstract

Nonlinear least squares optimization is used most often in fitting a complex model to a set of data. An ordinary nonlinear least squares optimizer assumes a constant variance for all the data points. This paper presents SENSOP, a weighted nonlinear least squares optimizer, which is designed for fitting a model to a set of data where the variance may or may not be constant. It uses a variant of the Levenberg-Marquardt method to calculate the direction and the length of the step change in the parameter vector. The method for estimating appropriate weighting functions applies generally to 1-dimensional signals and can be used for higher dimensional signals. Sets of multiple tracer outflow dilution curves present special problems because the data encompass three to four orders of magnitude; a fractional power function provides appropriate weighting giving success in parameter estimation despite the wide range.

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Authors and Affiliations

  1. Center for Bioengineering, University of Washington, WA 98185, Seattle, Washington

    I. S. Chan, A. A. Goldstein & J. B. Bassingthwaighte

Authors
  1. I. S. Chan
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  2. A. A. Goldstein
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  3. J. B. Bassingthwaighte
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Chan, I.S., Goldstein, A.A. & Bassingthwaighte, J.B. SENSOP: A derivative-free solver for nonlinear least squares with sensitivity scaling. Ann Biomed Eng 21, 621–631 (1993). https://doi.org/10.1007/BF02368642

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  • DOI: https://doi.org/10.1007/BF02368642

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