Computation Physics / Carleton University / Root Finding

Root Finding

The general problem of solving a nonlinear equation can be reexpressed as a problem of finding points where a function is zero. This section studies various methods for zeroing in on the root of the problem as quickly as possible. In one dimension, bracketing of the root is possible, and Ridders and Brent methods are good general purpose methods that converge on the solution very quickly. Roots of polynomial equations can be found using Laguerre's method.

The Newton-Raphson method requires knowledge of the function and its first derivatives. A diversion into fractals generated with the approach is included. The method can be used for multidimensional problems.

The exercise involves finding the maximum of a blackbody radiation spectrum.

Reference:

Numerical Recipies, chapter 9.

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