Newton’s method pth root- MATLAB -

newton’s method can used calculate p-th root of positive real number. write matlab function myrootp.m calculates a^(1/p) a> 0 , positive integer p. function should stop when abs((xk^(p)/a)-1)<10^(-15).

i used following code cannot find error:

   function root1 = root1( a,x0,p)      xk=x0;     fd= p*xk^(p-1);     f=(xk^p)-a;     if a<0  disp('error:a must positive , real')     else k=1:p     if abs(xk^p/a-1)<10^(-15)         return disp('error');     else                 xk1=xk-f/fd;     xk=xk1;     fd= p*xk^(p-1);     f=(xk^p)-a;     end end    end    root1 = xk;   return   end 

i'd point out unfamiliar algorithm finding nth root of number using newton's method.

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back problem, there 2 errors:

1. there no such keyword then in matlab. rid of it.
2. you'll want iterate until error specified. looping many times there power p, , it's highly possible algorithm can converge before then, or worst case require more iterations p converge.

making these 2 changes:

function root1 = root1(a,x0,p)  xk=x0; fd= p*xk^(p-1); f=(xk^p)-a; if a<0      disp('error:a must positive , real') else     while true         if abs(xk^p/a-1)<10^(-15)             break;         else                         xk1=xk-f/fd;             xk=xk1;             fd= p*xk^(p-1);             f=(xk^p)-a;         end     end end  root1 = xk; 

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to test out, using initial guess of 5 or x0=5, , want find square root of 10 (a = 10, p = 2), get:

>> format long g; >> root1(10, 5, 2)  ans =        3.16227766016838 

comparing matlab's sqrt function, get:

>> format long g; >> sqrt(10)  ans =        3.16227766016838