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May 22nd, 2010, 02:37 PM   #1
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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?
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May 22nd, 2010, 03:07 PM   #2
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Re: Choosing an initial approximation for newtons law

If you can bracket the root, then a short binary search will get you close.
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May 22nd, 2010, 05:03 PM   #3
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Re: Choosing an initial approximation for newtons law

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Originally Posted by mathman
If you can bracket the root, then a short binary search will get you close.
Sorry but I haven't done any binary search. Isn't there a simple way to do it?
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May 23rd, 2010, 12:26 PM   #4
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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.
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May 23rd, 2010, 12:27 PM   #5
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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 |b-a| is small enough.
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