Re: Reliable ComputingÙ absxÙ for intervals?
George Corliss wrote:
> Consider an ODE solver, say Runge-Kutta. If we change double to interval,
> we should get an interval that encloses what the RK code computes, but it
> is quite likely that we will get an interval that does NOT enclose the
> correct answer. If that happens, the user is likely to conclude that
> the interval community has lied; he did NOT get an enclosure of the true
> solution. He missed class the day the prof covered truncation errors?
I'm not sure I follow. Truncation errors should occur in both directions,
possibly eventually widening intervals to the point of uselessness, but
why would containment be violated? I have to admit that I have never
used RK (though I have heard of it, and browsed, but never seriously
studied, some numerical analysis textbooks), so perhaps I'm overlooking
something.
Are you perhaps assuming incorrect scalar->interval conversions,
i.e. replacement of 0.1 with
[+1.00000000000000006E-001, +1.00000000000000006E-001]
instead of
[+9.99999999999999917E-002, +1.00000000000000006E-001]
when converting the program (assuming Binary64-based arithmetic)?
Whatever IA extensions are added to the language, they must provide
means to avoid that kind of mistake.
Michel.
---Sent: 2009-04-15 21:13:13 UTC