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## Newton's Method

version 1.1.0.0 (1.39 KB) by
Finds better successive approximations for the root of a function using Newton's Method.

71 Downloads

Updated 11 Mar 2011

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This is still a work in progress, having trouble setting tolerances but setting the number of iterations seems to work fine.

### Cite As

Harmon Amakobe (2021). Newton's Method (https://www.mathworks.com/matlabcentral/fileexchange/30698-newton-s-method), MATLAB Central File Exchange. Retrieved .

### Comments and Ratings (6)

Madison Stephens

ahmad faisal

Hamza saeed khan

Thank you sir, it help me to pass exams becuase of you. Keep doing good work.

Trish Patel

Another submission to this method which my original.
% Newton Method for Finding Solution of equation Numerically

clear all;
close all;
clc;
fprintf('THE PROGRAM COMPUTES THE SOLUTION TO AN EQUATION f(x)=0 BASED ON NEWTONS METHOD GIVEN FUNCTION f, Required Accuracy,Number of iterations \n');
x=sym('x');
prompt = 'input a function: ';
f=input('f(x)='); % input as f

prompt = 'input the starting value of x or x0: ';
x0=input('x0='); % starting number

prompt = 'What is the max tolerance acceptable? ';
toll = input(prompt)% tolerance input
if (toll<=0) %error 1
fprintf( 'You cannot have a negative tolerance!! \n Program will exit now \n')
break
end

prompt = 'What is the max iteration? ';
iter = input(prompt)%Error 2
if (iter<=0)
fprintf( 'You cannot have a negative iteration!! \n Program will exit now \n')
break
end

fprintf('f(x)=');
disp (f); % input fucntion
f_dir=diff(f);
fprintf('f''(x)=');
disp (f_dir); % deravitive function

y=matlabFunction(f,'file','myfile'); % convert from Symbolic function to Matlab Function and stores in a file
ydir=matlabFunction(f_dir,'file','myfile_1'); % convert from Symbolic derivative to Matlab Function and stores in a file

out(1)=x0; % starting value
fprintf('n| xn | xn+1 | epsilon |\n');
for (i=1:iter) % converging

out(i+1)=out(i)-(myfile(out(i))/myfile_1(out(i))); %Newton Method
fprintf('%i|x%i=%f |x%i=%f |epsilon=(%f) |\n',(i-1),(i-1),out(i),i,out(i+1),abs(out(i+1)-out(i))); %shows the output in each iteration

if (abs((out(i+1)-out(i)))<=toll) % used for the condition to display the output
fprintf('Procedure completed successfully \n The solution converges to %f to 6D \n',(out(i+1)));%displays the final result of the convergence if it converges in 6D
break %Breaks program
end

if (myfile_1(out(i))==0)
fprintf('Failure \n procedure completed unsuccessfully')
fprintf('Please try with a different starting value of x0; Rerun program')
break
end

if (((iter-i)<=0)&&(abs((out(i+1)-out(i)))>=toll))%checks for the condition if the tolerance is not met
fprintf('Procedure completed unsuccessfully after N ierations \n Retry with more number of iretations and try a different starting value\n');
break
end
end
fplot(y,[-(x0) (x0)]); % plotting
hold on
grid on
fplot(ydir,[-(x0) (x0)],'r'); %plots the derivative function
title('Plot of f(x) and f''(x) in red')
hold off

% clear all; close all;

Andrew Knyazev

"Number of iterations will be increased accordingly in order to meet the set tolerance value" - in other words the "ite" parameter is always ignored. The code never stops if the tolerance is not met.

Thomas

Note that your m file requires symbolic tool box in order to use the sym function. Another way to do this is to do a numerical differentiation to get f'(x) instead.

##### MATLAB Release Compatibility
Created with R2010b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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