Main.m

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% 
% Not Complete
% 22/03/2021
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%% Cleaning
clear
clc

%% Input Function and Variables
func = @(x) x.^(2)+x-14;
dFunc = @(x) 2*x+1;
xl = -14;
xu = 0;
x1 = -14;
x2 = -13;
x3 = -12;
terminationCriteria = 0.00001;
maxIterations = 100;

%% Bracketing Methods - Bisection Method 
% (Binary Chopping - Bolzano's Method)
% The Bisection Method is an iterative application of IVT to numerically 
% determine roots of continuous functions. 
figure('Name','Bisection Method')
[rootValBisection,errorValBisection,iterNumbBisection,elapsedTimeBisection] = ...
    bisection(func,xl,xu,terminationCriteria,maxIterations);

%% Bracketing Methods - False-Position Method
% The False-Position Method is a modificiation of Bisection Method that is 
% needed due to Brute-Force approach and poor convergence of Bisection Method. 
figure('Name','False-Position Method')
[rootValFP,errorValFP,iterNumbFP,elapsedTimeFP] = ...
    falsePos(func,xl,xu,terminationCriteria,maxIterations);

%% Open Methods - Newton-Raphson Method
% The Newton-Raphson method is a widely used root-finding algorithm. Method
% successively and numerically obtains better results and approximations for the roots.
% It is based on the idea of linear approximation and named after Isaac Newton and Joseph Raphson. 
% For the derivative of the input function, 
% It might be useful to use diff + matlabFunction + sym instead.
figure('Name','Newton-Raphson Method')
[rootValNR,errorValNR,iterNumbNR,elapsedTimeNR] = ...
    newtonraphson(func,dFunc,xl,terminationCriteria,maxIterations);
    
%% Open Methods - Secant Method
% Secant Method does not require evaluation for the derivation, instead 
% it uses a finite difference to approximate the derivative. The Method 
% divides each interval by the secant line connecting to the endpoints. 
figure('Name','Secant Method')
[rootValSM,errorValSM,iterNumbSM,elapsedTimeSM] = ...
    secant(func,xl,x2,terminationCriteria,maxIterations);
    
%% Open Methods - Brent's Method
% Also known as Van Wijngaarden-Dekker-Brent Method.
% Brent's Method is a hybrid approach combining the Bisection Method and
% inverse quadratic interpolation; therefore, having reliability of
% bracketing methods and fast computing of open methods. 
% Brent's Method was developed by Richard Brent (1973).
figure('Name','Brents Method')
[rootValBM,errorValBM,iterNumbBM,elapsedTimeBM] = ...
    brents(func,x1,x2,x3,terminationCriteria,maxIterations);