From: David Abrahams (abrahams_at_[hidden])
Date: 2001-04-24 08:28:20
----- Original Message -----
From: "Peter Schmitteckert (boost)" <boost_at_[hidden]>
> On Tuesday 24 April 2001 12:53, Dave wrote:
> > > has (?) replaced char. (We only need to convince the performance
> > > freaks that there is little or no cost involved.)
> > Is that really possible? Surely one has to do 2-3 times as many
> > floating-point ops to handle intervals as raw numbers. I know that in my
> > application domain (simulation), nobody would be willing to pay that
> > Typically these simulations use iterative methods that only strive for a
> > few digits of accuracy before producing a result anyway.
> Well, you can use better algorithms.
> Suppose you want to calculate a zero of a function f(x).
> You will need just one function call to check if x has a
> zero in the interval -1..1:
"just one function call" could mean millions of instructions. Did you mean
to say something else?
> if f( interval<double>(-1,1) ) contains no zero then it is proven that
> is no zero.
Knowing that a zero exists doesn't help me to find the zero, does it?
Knowing that no zero exists might be useful so that I can give up and try
something else, but it doesn't solve my main problem, which is finding x
s.t. f(x) = 0 when such a zero does exist.
> Try to do this without interval arithmetics. Extending this
> should be clear.
I have no argument that interval arithmetic is useful. It's just unclear to
me that its useful for solving the type of problem I'm working on, much less
a substitute for single-valued calculations in all circumstances.
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