Newton Raphson Method!!!

Hi,

I'm trying to run the Newton Raphson method for 3 different initial values. 5 iterations for each value. I'm trying to get results stored as r1,r2,r3. So far only r1 looks ok but the other 2 are 0 which is wrong. Any help would be appreciated.

[r1,r2,r3] = newton();
function [r1,r2,r3] = newton()
r1= 0;
r2=0;
r3=0;
r = [r1 , r2 , r3]; 
x0= [0.5,1.5,2.5];
x= [ 0 , 0 , 0 ];

i=0; 
j=1:3;
for j= 1:3;
    f = x0(j)^4 - 9*x0(j)^3+29*x0(j)^2-39*x0(j)+18;
df = 4*x0(j)^3 - 27*x0(j)^2 +58*x0(j) -39;  
while i < 5
    i= i+1; 
     x(j) = x(j) - f/df;
    x0(j) = x(j);
    
    disp (r1);
    if i==5
        r(j)=x0 (j); 
        disp('root is');
        disp(r); 
        break
    end
        
end
end

end 

Answer 1

[David Hill]

function x = newton()
x=[0.5,1.5,2.5];
f=[1,-9,29,-39,18];
df=polyder(f);
for j= 1:5
   x = x - polyval(f,x)./polyval(df,x);
end

[alexp10]

Im confused, this just gives me ones. Do you know where I need to put this in my code?

[David Hill]

It gives you the roots from all three of your initial starting points. If f is not a polynominal, you will need to change it to whatever the function is as well as df. You should be getting x =

0.999999992597444   1.999999942243890   3.020841456431222

[David Hill]

The loop is performing all the calculations at once doing element-wise calculations of the arrays.

[alexp10]

Thankyou