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Nonlinear Methods

In: Scientific Data Analysis

Author

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  • Richard L. Branham Jr.

    (Jefe Area Matematicas y Del Centro Regional de Investigaciones Científicas y Tecnológicas)

Abstract

Sometimes our problem involves nonlinear equations. If, for example, we wish to determine the half-life of a radioactive nuclide. In the p-norm the equations assume the form 7.1 $$ {{\left\| {{{A}_{o}}{{e}^{{ - \lambda {{t}_{i}}}}} - {{A}_{i}}} \right\|}_{p}} = \min , $$ where A o is the original quantity of nuclide at time t o = 0, Ai is the quantity at time t i and λ is the half-life to be determined. Physical chemistry offers the Michaelis-Menten equation: X i is the concentration of an enzyme with a reaction rate t i and we wish to determine constants a and b such that 7.2 $${\left\| {\frac{{a{X_i}}}{{b + {X_i}}} - {y_i}} \right\|_p} = \min .\,$$

Suggested Citation

  • Richard L. Branham Jr., 1990. "Nonlinear Methods," Springer Books, in: Scientific Data Analysis, chapter 0, pages 168-198, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3362-6_7
    DOI: 10.1007/978-1-4612-3362-6_7
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