Posted by **geoff** on Sunday, October 16, 2011 at 11:54am.

imagine you have a simple calculator that can only do addition,subtraction,multiplication and division. show how you can still use it to calculate the cube root of a given number, ie a^1/3, as follows:

a)show that newton raphsons method for solving the equation x^3 -a=0 results in the iteration

X(n+1)=(2/3)X(n) + a /(3X^2(n)

b)illustrate the method by calculating the cube root of a=10, starting at,

x(1)=2 and iterating until the absolute error compared to the previuos step becomes less than 1*10^-12. show the iterations, the result of each and its relative error . How many iterations did you need for convergence?

What are the absolute and relative errors of your solutions compared to the actual answer(as given by matlab)?

c)solve the same question with the same precision as in part b), using the bisection method starting with the bracketing interval [2:3] and the secant method starting again at x(1)=2.

how many iterations did you need in each case ?

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