Nonlinear Methods

Richard L. Branham
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Richard L. Branham: Jefe Area Matematicas y Del Centro Regional de Investigaciones Científicas y Tecnológicas

Chapter Chapter 7 in Scientific Data Analysis, 1990, pp 168-198 from Springer

Abstract: 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 $${\left\| {\frac{{a{X_i}}}{{b + {X_i}}} - {y_i}} \right\|_p} = \min .\,$$

Keywords: Gradient Method; Hessian Matrix; Simplex Method; Nonlinear Method; Steep Descent Method (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-1-4612-3362-6_7

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