jburkardt

CYCLE_BRENT\ Cycle Detection by Brent’s Method {#cycle_brent-cycle-detection-by-brents-method align=”center”} =================================


CYCLE_BRENT is a C++ library which analyzes a cycle in an iterated function sequence using Brent’s method.

Suppose we a repeatedly apply a function f(), starting with the argument x0, then f(x0), f(f(x0)) and so on. Suppose that the range of f is finite. Then eventually the iteration must reach a cycle. Once the cycle is reached, succeeding values stay within that cycle.

Starting at x0, there is a “nearest element” of the cycle, which is reached after MU applications of f.

Once the cycle is entered, the cycle has a length LAM, which is the number of steps required to first return to a given value.

This function uses Brent’s method to determine the values of MU and LAM, given F and X0.

Licensing: {#licensing align=”center”}

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages: {#languages align=”center”}

CYCLE_BRENT is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a PYTHON version.

CYCLE_FLOYD, a C++ library which carries out an iterated function evaluation, and seeks to determine the nearest element of a cycle, and the cycle’s length, using Floyd’s method.

Reference: {#reference align=”center”}

  1. Richard Brent,\ An improved Monte Carlo factorization algorithm,\ BIT,\ Volume 20, Number 2, 1980, pages 176-184.

Source Code: {#source-code align=”center”}

Examples and Tests: {#examples-and-tests align=”center”}

List of Routines: {#list-of-routines align=”center”}

You can go up one level to the C++ source codes.


Last revised on 17 June 2012.