Re: back to the roots
Bill,
No. Such interval libraries returns a sharp bound on the narrowest
possible interval that encloses the given function over any given
non-degenerate interval argument.
Hypothetical question: If practical input arguments are only accurate to
4 decimal digits, then why bother to compute function values to high
precision of low accuracy?
One reason is that even though data may be known to be inaccurate,
computations are nevertheless performed with floating point numbers. I
think that keeping the influence of roundoff errors as small as possible
is not only of academic interest, but also a practical concern. Accurate
elementary functions are one means to achieve this, and so is an exact
dot product.
Regards,
Markus