Newtons method for finding minimum of a function.

I want to mark the solution point (x,f(x)) obtained by the Newton's algorithm on the curve of the function f(x)=(e^(2*sinx))-x to see if it is a local minimum or something else, but I am stuck. I used myfunction in order to obtain the function value and its derivatives Can someone help me with this? I will show you what I have so far.

			% Clears all data and screen
clear;
close all;
clc;
 
f1 = @(x) exp(2*sin(x))-x;              %function 
x0 = 3;                                 %initial guess
 
maxIter = 1e6;                          %max iteration of the function
epsilon = 10e-6;                            %tolerance value
 
 
% Calling the Newton's Method function
[xk,i,error,errorVect] = NewtonsMethod(x0,maxIter,epsilon);
 
% Printing Newton's Method Results in the console
fprintf('\nThe solution of the function exp(2*sin(x))-x = 0 is %4.5f in %u iteration with %e error.\n', xk,i,error)
xk;
ymin = f1(xk);
errorVect;
% Function for Newton's Method function
 
 
 
%Graphing the error vector
x_axis = 1:1:length(errorVect);                     %x-axis values
semilogy(x_axis,errorVect,'-mo');       %graph of error vector in logarithmic y-axis
grid on                                 %logarithmic grid (y-axis only)
 
function[xk,i,error,errorVect] = NewtonsMethod(xk,maxIter,epsilon)
    xold = xk;
    for i = 1:maxIter
        [f1x,df1x,ddf1x]=myfunction(xk);
        xk = xk - (df1x/ddf1x);
        
        error = abs(xk-xold);
        xold = xk;
        errorVect(i) = error;
        if  (error<epsilon)
            break;
        end
    end
end
 
% Function for calling the value and the derivative of the function
function [f,g,h] = myfunction(x)
    f1 = @(z) exp(2*sin(z))-z;                  %function
    f = f1(x);
    syms z
    if nargout > 1
        g1(z) = diff(f1(z));
        g = double(g1(x));
        h1(z) = diff(g1(z));
        h = double(h1(x));
    end
end
				
					

				
			

[Jim Riggs]

It will be much easier for people to read your code and help you if you use the formatting buttons to format your code.

Or, simply select your code and press <alt> <enter> to format it. Try it.

[Jim Riggs]

for your myFunction, try the following;

function [f,g,h] = myfunction(x)
    f1 = @(z) exp(2*sin(z))-z;                  %function
    ff = f1([x-1, x, x+1]);    % this is a 3-element vector
    f = ff(2);                 % the middle value is f1(x)
    if nargout > 1  % (not sure why you use this)
        gg = diff(ff);    % this is a 2-element vector from diff(ff)
        g = mean(gg);
        h= diff(gg);      % single value from diff(gg)
    end
end

Answer 1

[Jim Riggs]

Here is another variation;

function [f,g,h] = myfunction(x)
    f1 = @(z) exp(2*sin(z))-z;                  %function
    dx = 0.1;
    ff = f1([x-dx, x, x+dx]);    % this is a 3-element vector
    f = ff(2);                  % the middle value is f1(x)
    if nargout > 1  % (not sure why you use this)
        gg = diff(ff)./dx;    % this is a 2-element vector from diff(ff)
        g = gg(1);
        h= diff(gg)./dx;      % single value from diff(gg)
    end
end