Re: Looking for suggestions on a root search strategy

In article <459b0a7b$0$8994$4c368faf@xxxxxxxxxxxxxx>,
Alan <info@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
I would appreciate any suggestions on a
good algorithm for finding a root with the following setup:

My real-valued function f(x) either
(i) has no roots in (0,a) or
(ii) has a single root x = b in (0,a), where 0 < b < a

-But-, in case (ii), my function is undefined for x > b.

Other things I know about my function:
f(0) < 0; but f''(x) may have either sign.

I want to efficiently return either the single root or, let's say
some indicator if there are no roots.
The puzzle to me is how to avoid evaluations
of f(x) where it is undefined. Assume that if this happens,
your computer crashes.
If f(x) were concave downward, a
Newton's method iteration would work, but sometimes I have
opposite or mixed concavity.

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''?

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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