Richard Fateman <fateman at eecs.berkeley.edu> writes:
> oops. here's the link
> RJF
>
> http://www.eecs.berkeley.edu/~wkahan/Math128/SOLVEkey.pdf
I was thinking about this a bit after reading the linked article. I
agree with the (clever and short) proof that a "black box" equation
solver can't possibly always work.
However, programs like Maxima are often given formulas. Is there
research about numerical root finding for, say, rational expressions or
maybe ones containing trig functions, logarithms etc? Then your
functions are analytic and you've got a hope of spotting icky points in
the denominator etc. etc...
Presumably an ideal computer root finder would be able to say something
like:
"I have found <n> roots, which lie in the following (tiny)
intervals. There are possibly up to <m> other roots that I haven't
found."
Have people worked on this?
Rupert
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