Write a function to calculate the cubic root of a 2D array

(This is a homework question, so I'm not supposed to use nthroot except to check my answer). 

An algorithm for calculating the cubic root of a number, 3√? , starts by choosing a value ?1 as a first estimate of the root. Using this value, a second, more accurate value ?2 is calculated as ?2 = ?1 (?1^3 + 2?)/(2?1^3 + ?), which is then used for calculating a third, still more accurate value ?3, and so on. The general equation for calculating the ? + 1 value from the ? ?ℎ value of ? is ??+1 = ?? (??^3 + 2?)/(2??^3 + ?).

I am supposed to be writing a function using two for loops and a while loop to calculate the cube root of a 2D array. My function so far will work for the first few numbers of a matrix, but "gives up" halfway through and gives incorrect answers. Can anyone tell me why this is happening? (The equation in the while loop is given to us, and I double checked it already, and E is for the error).

F = [1:5; 10:-1:6; 11:15]

function [Root3] = HW7P2_fn(matrix)
% Function to determine cubic root of a number
% Input value is the number whose cubic root is needed
% Output value is the cubic root

clc
[i, j] = size(matrix);
Root3 = zeros(i,j);
n = 1;

for rows = 1:i
    for cols = 1:j
        P = matrix(rows,cols);
        xi = P;
        while n <= 50
            xip1 = (xi*(xi^3 + 2*P))/(2*(xi^3) + P);
            Root3(rows,cols) = xip1;
            E = abs((xip1 - xi)/xi);
            
            if E < 10e-10
                break
            end  
            
            xi = xip1;            
            n = n+1;           
        end
    end
end
end

Answer 1

[Sriram Tadavarty]

Hi Leah,

Update the while loop variable n to 1 within the second for loop. This is the issue with half way wrong answer. The index is not getting initialized for each element in the matrix. See the change in below code.

function [Root3] = HW7P2_fn(matrix)
% Function to determine cubic root of a number
% Input value is the number whose cubic root is needed
% Output value is the cubic root
clc
[i, j] = size(matrix);
Root3 = zeros(i,j);
%n = 1; THis has to be placed within the second for loop
for rows = 1:i
    for cols = 1:j
        P = matrix(rows,cols);
        xi = P;
        n = 1; % It should start from 1 for every element.
        while n <= 50
            xip1 = (xi*(xi^3 + 2*P))/(2*(xi^3) + P);
            Root3(rows,cols) = xip1;
            E = abs((xip1 - xi)/xi);
            
            if E < 10e-10
                break
            end  
            
            xi = xip1;            
            n = n+1;           
        end
    end
end
end

Hope this heps.

Regards,

Sriram