The function should starts as:
function [x,fs,k]=Newton1(x0)
% enter your code here
end
>> [x,f,k]=Newton1(0) x = 1.1641, f = -1.6653e-16, k = 7
>> [x,f,k]=Newton1(0.1) x = 0.1972, f = 1.1102e-16, k = 5
>> [x,f,k]=Newton1(1.5) x = 1.3111, f = -1.1102e-16, k = 6
>> [x,f,k]=Newton1(2) Warning iteration diverged, x = 2.8808, f = -0.5624, k = 1000
%%% Function %%
function [ xz fs k ]=Newton1(x0)
format long
tol=5*eps;
c(1)=x0;
syms x;
f=exp(-0.5*x)*cos(5*x)-0.5 ;
for k=1:1000
l1=subs(f,c(k));
l2=subs(diff(f),c(k));
c(k+1)=c(k)-l1/l2;
l3=(subs(f,c(k+1)));
fs=l3;
xz=c(k+1);
if (abs(l3) < tol)
break;
end
end
end
%%% Test %%%
[x fs k]=Newton1(0);
fprintf(' x= %f \n',x);
fprintf(' fx= %1.32f \n',fs);
fprintf(' k= %f \n',k);
if k>1000
fprintf('Iteration diverged');
end
OUTPUT:
x= 1.164097
fx= -0.00000000000000006861264023336157
k= 7.000000
>>
%%%Test
clc;
close all;
clear all;
format long;
[x fs k]=Newton1(1.5);
fprintf(' x= %f \n',x);
fprintf(' fx= %1.32f \n',fs);
fprintf(' k= %f \n',k);
if k>1000
fprintf('Iteration diverged');
end
OUTPUT:
x= 1.311127
fx= -0.00000000000000002916434802119459
k= 6.000000
%%%Test
clc;
close all;
clear all;
format long;
[x fs k]=Newton1(2);
fprintf(' x= %f \n',x);
fprintf(' fx= %1.32f \n',fs);
fprintf(' k= %f \n',k);
if k>1000
fprintf('Iteration diverged');
end
OUTPUT:
x= 2.399596
fx= -0.24611144691801684070142641758139
k= 1000.000000
Iteration diverged>>
The function should starts as: function [x,fs,k]=Newton1(x0) % enter your code here end >> ...
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