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 ?

## Answer This Question

## Related Questions

- Algebra PLEASE? - Using the numbers 5, 8, and 24, create a problem using no more...
- math - Using the numbers 5, 8, and 24, create a problem using no more than four...
- another one ASAP - using the number 5, 8, and 24, create a problem using no more...
- Math, algebra!! Please help!!!!!! - Using the numbers 5, 8, and 24, create a ...
- Algebra 8th grade please help!!!!!! - Using the numbers 5, 8, and 24, create a ...
- computer programming - Make an Maplet that does the simple calculator funtions ...
- math - using exactly four 4s and only addition, subtraction, multiplication, and...
- math - How can you make 34 by only using the digits 1, 2, 3, and 4? You can put ...
- math - 115-100+3*5= 115-100+3*5...Use BEDMAS (Bracket, Exponent, Division/...
- math - How can you make 7 by only using the digits 1, 2, 3, and 4? You can put ...

More Related Questions