One numerical method for calculating the cubic root of a number VX is by using i

Question

One numerical method for calculating the cubic root of a number VX is by using iterations. The process starts by choosing a value xi as a first estimate of the solution. Using this value, a second a more accurate value x2 can be calculated with X2 + 2x) /3, which is then used for calculating a third, and more accurate value xs, and so on. The general equation for calculating the value of xii from x, is i+1 Write an m-file which uses x 100 as the first estimate to calculate the cube-root of 100 (x -the cube root of the number you're calculating). Stop the looping when the relative error with each iteration is smaller than le-5. le. E = and print out the value using fprintf. smaller than le-s. le.EDetermine the number of iterations required to achieve this criterion E.g. The number of iterations required is 16 and the cube root of 999 is 9.996666, using x1-999.

Explanation / Answer

//take random input to find out cube root

x1= input()

prev = x1;

//initialize count which count number of iteration

count=0;

while(1)

{

new = ((num/(prev*prev))+2*prev)/3

count++;

E = (new-prev)/prev;

if(new<E)

break;

}

fprintf("the number of iteration required is %d and the cube root of %4.2f is %4.2f,using x1=%d",count,num,x1);

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