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 12 Replies  3709 Views  Last Post: 12 July 2009  09:18 AM
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 NewtonRaphson 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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