BIT Numerical Mathematics

, Volume 19, Issue 2, pp 214–222 | Cite as

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

  • F. M. Larkin


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.


Gaussian Distribution Probability Distribution Hilbert Space Computational Mathematic Maximum Likelihood Estimate 
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Copyright information

© BIT Foundations 1979

Authors and Affiliations

  • F. M. Larkin
    • 1
  1. 1.Dept. of Computing and Information ScienceQueen's UniversityKingstonCanada

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