%**** Examples from Chapter 05 ****'));


%'**** Example 5.7 Interval Bisection *'));
% Find the root of nonlinear equation f(x)=x^2-4sin(x)=0
% by interval bisection using initial bracket [a b] is [1 3]
% Iterate until the tol = 10^(-4) is achieved and dump intermediate results.
% How many iterations are needed?	
% Check your result using Matlab function "fzero".


%'**** Example 5.x Fixed Point Iteration *'));
% Solve the same problem by Fixed Point Iteration. 


%'**** Example 5.10 Newton's Method *'));
% Solve the same problem by Newton's Method. 


%'**** Example 5.12 Secant Method *'));
% Solve the same problem by Secant Method.
% Compare the number of iterations for all implemented methods and select the best one for this case.



%'**** Example 5.15 Newton's Method for n-dimensions *'));
% Find the roots of 2-dimensional function F(x)=[x_1+2x_2-2; x_1^2+4x_2^2-4]'
% using initial guess x0=[1 2]';  


%'**** Example 5.16 Broyden's Method for n-dimensions *'));
% Solve the system from 5.15 again by Broyden's Method and compare the number of iterations
% for the same tolerance.