code C++ to find function f(x)=0 "with newton method and secan method"

# C++ HW: Find function f(x)=0 with Newton method

## code C++ to find function f(x)=0 "with newton method and secan me

Page 1 of 1## 2 Replies - 5786 Views - Last Post: 12 July 2009 - 09:18 AM

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**Replies To:** C++ HW: Find function f(x)=0 with Newton method

### #2

## Re: C++ HW: Find function f(x)=0 with Newton method

Posted 12 July 2009 - 08:30 AM

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### #3

## Re: C++ HW: Find function f(x)=0 with Newton method

Posted 12 July 2009 - 09:18 AM

Well first you need to know a little more about the Newton-Raphson method which is basically a simple iterative algorithm for finding a root of a function given a "best guess".

To use Newton's method you need to know the derivative of the function -- while for basic polynomials it is pretty easy to compute the derivative - in general this is not an easy task - I would imagine that your assignment does not mean you to program that part -- UNLESS you are taking a numerical method's class - in which case you may need to calculate the approximate value of f'(x).

so all you need to do is make write x = x - f(x)/f'(x) into a loop, initialize x with a "best guess" and then let it go, when you find that x does not change (or changes less than some degree of error) then you know that you have found a root (or an approximate value of a root).

You may also want to set a maximum number of iterations, since in instances Newton's Method will not converge.

The secant method does not require the derivative, but its convergence will be slower than Newton's method -- but here we need to have two guesses. x and ox

nx = x - f(x)*(x - ox)/(f(x)-f(ox)); ox = x; x = nx;

(here ox stood for "old x" and tx stood for "new x").

Note that the secant method is just Newton's method with a trick to approximate the derivative.

To use Newton's method you need to know the derivative of the function -- while for basic polynomials it is pretty easy to compute the derivative - in general this is not an easy task - I would imagine that your assignment does not mean you to program that part -- UNLESS you are taking a numerical method's class - in which case you may need to calculate the approximate value of f'(x).

so all you need to do is make write x = x - f(x)/f'(x) into a loop, initialize x with a "best guess" and then let it go, when you find that x does not change (or changes less than some degree of error) then you know that you have found a root (or an approximate value of a root).

You may also want to set a maximum number of iterations, since in instances Newton's Method will not converge.

The secant method does not require the derivative, but its convergence will be slower than Newton's method -- but here we need to have two guesses. x and ox

nx = x - f(x)*(x - ox)/(f(x)-f(ox)); ox = x; x = nx;

(here ox stood for "old x" and tx stood for "new x").

Note that the secant method is just Newton's method with a trick to approximate the derivative.

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