Question

Problem 1 (30 points) An efficient way of computing the cube root of a number N is to compute the root of 3 f(x) = x³ - N = 0 with the method of Newton Raphson, namely: $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$ Combining the two equations and rearranging terms gives the recursive (iterative) relationship $x_{n+1} = \frac{1}{3} \cdot \left[ \frac{2x_n^3 + N}{x_n^2} \right]$ where $x_{n+1}$ is the next guess or iteration. Write a MATLAB program that will prompt the user for a number N and compute the cube root of N via the Newton Raphson technique above and use the simple convergence test $\left| \frac{x_{n+1} - x_n}{x_n} \right| \le \epsilon$ Where $\epsilon$ is some very small number, say 0.000001. The program should then display the number N, its cube root, and the number of iterations needed to compute the result.

          Problem 1 (30 points)
An efficient way of computing the cube root of a number N is to compute the root
of
3
f(x) = x³ - N = 0
with the method of Newton Raphson, namely:
$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$
Combining the two equations and rearranging terms gives the recursive (iterative)
relationship
$x_{n+1} = \frac{1}{3} \cdot \left[ \frac{2x_n^3 + N}{x_n^2} \right]$
where $x_{n+1}$ is the next guess or iteration. Write a MATLAB program that will
prompt the user for a number N and compute the cube root of N via the Newton
Raphson technique above and use the simple convergence test
$\left| \frac{x_{n+1} - x_n}{x_n} \right| \le \epsilon$
Where $\epsilon$ is some very small number, say 0.000001. The program should then
display the number N, its cube root, and the number of iterations needed to
compute the result.

Problem 1 (30 points)
An efficient way of computing the cube root of a number N is to compute the root
of
3
f(x) = x³ - N = 0
with the method of Newton Raphson, namely:
xn+1 = xn - (f(xn))/(f'(xn))
Combining the two equations and rearranging terms gives the recursive (iterative)
relationship
xn+1 = (1)/(3)·[ (2xn^3 + N)/(xn^2)]
where xn+1 is the next guess or iteration. Write a MATLAB program that will
prompt the user for a number N and compute the cube root of N via the Newton
Raphson technique above and use the simple convergence test
| (xn+1 - xn)/(xn)| ≤ϵ
Where ϵ is some very small number, say 0.000001. The program should then
display the number N, its cube root, and the number of iterations needed to
compute the result.

Added by Jacqueline L.

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