%% Newton method matlab sample Examples
%Dejen Ketema,  March,2019. %f = @(x)(x/2).^2-sin(x);
%% Example 1 convergence
%  f=@(x)x.^2-1;
%  df=@(x)2*x;
% p0=4;
%  tol=.0001;
%  xmin=0;
%  xmax=3;
% p=newton_table_2019(f,df,p0,tol);
%%Example 2 

%%Drawbacks of the Newton-Raphson Method 
 %%Root jumping 
%   f=@(x)sin(x);
%    df=@(x)cos(x);%
% p0=1;
%  tol=.0001;
%  xmin=0;
%  xmax=3;
% p=newton_table_2019(f,df,p0,tol);
%% Divergence at inflection points
% f=@(x)(x-1).^3+0.512;
%  df=@(x)3*x(x-1).^2;
% p0=10;
%  tol=.0001;
%  xmin=0;
%  xmax=3;
% p=newton_table_2019(f,df,p0,tol);
%%Division by zero 
%  f=@(x)x.^3-0.03*x.^2+2.4* 1.0000e-06;
%  df=@(x)3*x.^2-0.06*x;
%  p0=4;
%  tol=.0001;
%  xmin=0;
%  xmax=3;
% p=newton_table_2019(f,df,p0,tol);
%%Oscillations near local maximum and minimum 
 %f=@(x)x.^3-2*x.^2-1;
 %df=@(x)3*x.^2-4*x;
%f=@(x)x.^2-x-1;
%df=@(x)2*x-1;
f=@(x)x.^2-4;
df=@(x)2*x;
p0=1;
 tol=0.1;
p=newton_table_2019(f,df,p0,tol);