Re: Looking for suggestions on a root search strategy


"Robert Israel" <israel@xxxxxxxxxxx> wrote in message
news:enffl7$6u0$1@xxxxxxxxxxxxxxxxxxxxxxxxx

Without any additional information, I don't see how it's
possible to avoid evaluating f or its derivatives at points
where it might be undefined. Might you, e.g., have an upper
bound on f''?

Thanks, Robert. You're right -- I need to specify more.
Let's assume that both f'(x) and f''(x) have an upper bound.

With f'(x) < |C|, say, then one could pick a small eps < |C| delta and
evaluate
f(eps), f(2 eps), f(3 eps), ... until the answer is zero to my tolerance
delta
without an illegal function evaluation. Of course, this method is grossly
inefficient,
requiring (r/eps) function evaluations for the root at r, whereas Newton's
method (if you could use it) typically only takes a few.

So, my revised query is for a reasonably efficient strategy given these
derivative bounds.

regards,
alan



.

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