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Re: Reliable ComputingX absxX for intervals?

Michel Hack schrieb:

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? 

The point is that a valid answer must also take account of the
discretization error, while a standard RK method with step size control simply uses fallible heuristics to decide when this error seems to be 
small enough.


Arnold Neumaier