A MATLAB implementation of the BDQRF root-finding algorithm

MATLAB function for calculating the single real root of a non-linear function using the Bisected Direct Quadratic Regula Falsi method.

This submission is a MATLAB implementation of the derivative-free Bisected Direct Quadratic Regula Falsi numerical method described in Vol. 4, 2010, no. 15 of Applied Mathematical Sciences by Robert G. Gottlieb and Blair F. Thompson. The companion zip archive also includes a MATLAB script named demo_bdqrf that solves the seven example functions described in the reference. The MATLAB version was created from the pseudocode provided by the authors.

The syntax of this MATLAB function is as follows;

function [x, y] = bdqrf(f, x1, x2, rtol)

% solve for a single real root of a nonlinear equation

% Bisected Direct Quadratic Regula Falsi (BDQRF)

% Applied Mathematical Sciences, Vol. 4, 2010, no. 15

% input

% f = objective function coded as y = f(x)

% x1 = lower bound of search interval

% x2 = upper bound of search interval

% rtol = algorithm convergence criterion

% output

% x = real root of f(x) = 0

% y = function value at f(x) = 0