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May 22nd, 2010, 02:37 PM  #1 
Member Joined: Apr 2010 Posts: 91 Thanks: 0  Choosing an initial approximation for newtons law
How would you guess a reasonable initial approximation, without missing, or being too far away from the root? (without graphing the function), when using Newton's law?

May 22nd, 2010, 03:07 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,707 Thanks: 674  Re: Choosing an initial approximation for newtons law
If you can bracket the root, then a short binary search will get you close.

May 22nd, 2010, 05:03 PM  #3  
Member Joined: Apr 2010 Posts: 91 Thanks: 0  Re: Choosing an initial approximation for newtons law Quote:
 
May 23rd, 2010, 12:26 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,375 Thanks: 2010 
You don't need an accurate graph of the function, but you do need to know enough about the graph to make a rough guess as to where a zero lies. Even if your rough guess is quite close, you may be unable to converge on the zero when using your rough guess as the initial estimate for Newton's method.

May 23rd, 2010, 12:27 PM  #5 
Global Moderator Joined: May 2007 Posts: 6,707 Thanks: 674  Re: Choosing an initial approximation for newtons law
The basic idea if you have brackets, say a and b where f(a)f(b) < 0. Then let c=(a+b)/2. Compute f(c) and replace a or b by c, depending on which f has the same sign as f(c). Continue until ba is small enough.


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