Numerical Root Finding Using the Newton-Raphson Algorithm

03/04/24 20:29 C:\Users\USERE PC\Downloads\fungsi.m 1 of 1

function y = fungsi (x) y = 25*x + 7 + x^3;

end

03/04/24 20:30 C:\Users\USERE PC\Downloads\raphson.m 1 of 1

clear; clc;

%% nilai parameter x1=1;

ErrorToleransi=0.00001;

ErrorRelatif=1;

xm0=1;

it=0;

%% header

fprintf('====================================================== \n') fprintf(' iterasi xm error r Interval \n')

fprintf('====================================================== \n')

%% algoritma newton raphson

while ErrorRelatif > ErrorToleransi it=it+1;

Fx=fungsi(x1);

Fdiff= (fungsi(x1 + ErrorToleransi)-Fx)/ErrorToleransi;

xm=x1-(Fx/Fdiff);

if abs(xm-x1) < ErrorToleransi root = xm;

return else

x1=xm;

end

ErrorRelatif = abs((xm0-xm)/xm0);

xm0=xm;

fprintf(' %d %f %f (%f;%f) \n', it,xm,ErrorRelatif,x1,Fx) end

MATLAB Command Window Page 1

======================================================

iterasi xm error r Interval

======================================================

1 -0.178570 1.178570 (-0.178570;33.000000) 2 -0.279386 0.564575 (-0.279386;2.530052) 3 -0.279130 0.000918 (-0.279130;-0.006470)

>>

MATLAB Workspace Page 1

03-Apr-2024 8:30:15 PM

Name Value

ErrorRelatif 9.1774e-04 ErrorToleransi 1.0000e-05

Fdiff 25.2337

Fx -5.2937e-08

it 4

root -0.2791

x1 -0.2791

xm -0.2791

xm0 -0.2791