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A modification of the secant rule derived from a maximum likelihood principle

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Abstract

An estimate of a zero of a complex function, constructed from ordinate information at distinct abscissae, is found from a Maximum Likelihood estimate relative to a normal probability distribution induced by a weak Gaussian distribution on a related Hilbert space. In the case of two ordinate observations this leads to an estimator structurally similar to the Secant Rule, and asymptotically approaching that rule in certain limiting situations. A correspondingly modified version of Newton's method is also derived, and regional and asymptotic convergence results proved.

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Authors and Affiliations

  1. Dept. of Computing and Information Science, Queen's University, Kingston, Ontario, Canada

    F. M. Larkin

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  1. F. M. Larkin
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Larkin, F.M. A modification of the secant rule derived from a maximum likelihood principle. BIT 19, 214–222 (1979). https://doi.org/10.1007/BF01930851

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  • DOI: https://doi.org/10.1007/BF01930851

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