Nonlinear Methods

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

$$ {{\left\| {{{A}_{o}}{{e}^{{ - \lambda {{t}_{i}}}}} - {{A}_{i}}} \right\|}_{p}} = \min , $$

(7.1)

where A _o is the original quantity of nuclide at time t _o = 0, A_i 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

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

(7.2)