If f(x)=0 has multiple roots,how is N-R method affected?How can N-R formula be modified to avoid this problem

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- Aug 13th 2006, 12:06 PMbobby77calculus- plz help..
If f(x)=0 has multiple roots,how is N-R method affected?How can N-R formula be modified to avoid this problem

- Aug 13th 2006, 12:30 PMdan
is N-R for Newton's method ? i.e. x_(n+1) = x_n-(f(x_n)/(f'(x_n))

dan - Aug 13th 2006, 11:35 PMGlaysher
If you mean Newton-Raphson then multiple roots is a common problem of any iterative method. Different starting values may give different solutions. Sketching the graph gives you a good idea of what starting values to try but the shape of the graph will determine how good N-R is and in some situations it doesn't work at all.

- Aug 14th 2006, 05:37 AMdan
if f(x)=0 then f'(x)=0 so N-R method would give you x_n-(0/0) so i dont think you can use it

- Aug 14th 2006, 06:03 AMGlaysher
That isn't true

eg f(x) = 2x - 2

= 0 at x = 1

f'(x) = 2 at all points not 0 - Aug 14th 2006, 06:10 AMdan
you said f(x)= 0 i.e f(x)= x-x or say f(x)=(x/(x^2))-(1/x) in any case f'(x)=0

- Aug 14th 2006, 07:40 AMGlaysher
He means solutions to the equation f(x) = 0 not define f(x) = 0. f(x) has not been defined. He wants a refined method for a general solution.

- Aug 14th 2006, 07:48 AMThePerfectHackerQuote:

Originally Posted by**bobby77**

**cannot**be another solution on this interval. Thus, if the function satisfies the condition for the Newton-Raphson algorithm then it will converge to that root.

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Here is a list of steps.

1)Find an interval $\displaystyle [a,b]$ such as, $\displaystyle f(a)f(b)<0$. (Gaurentees existence of a root).

2)Confirm that $\displaystyle f'(x)$ has only one sign. If not try chaning step #1 slightly to adjust step #2. (Gaurentees uniquesness of a root).

3)Select any point on $\displaystyle [a,b]$.

4)Algorithm will converge to that solution on that interval.. - Aug 14th 2006, 07:50 AMdanQuote:

Originally Posted by**Glaysher**

dan