4
$\begingroup$

For unums, there is good evidence (see figure 5) that accuracy is better than IEEE floats. (Note: I use the term "unum" broadly to refer to any of the various iterations and revisions to the format.)

However, generally we regard "stability as more of a constraint than accuracy". Are there numerical algorithms which can be made stable using some unum format that is unstable using IEEE floating point?

Improve this question
$\endgroup$
18
  • $\begingroup$ In your experience, can unums be largely described as (variable length) multi-precision intervals, so that algorithms, correctly implemented, return the "best possible" approximation and a correct (possibly too pessimistic) error bound? $\endgroup$
    – Lutz Lehmann
    Apr 28, 2022 at 5:41
  • 2
    $\begingroup$ Implicit in the question is "given that we're put so much effort into hardware implementations of IEEE floating point, would there be any real benefit to doing a hardware implementation of unums?" $\endgroup$
    – user14717
    Apr 28, 2022 at 17:07
  • 2
    $\begingroup$ Maybe start by asking the reverse question: What numerical algorithms currently suffer because they are using FP numbers that provide insufficient accuracy? (I can't think of much in this regard, but it's also not exactly my field.) $\endgroup$
    – Wolfgang Bangerth
    Apr 28, 2022 at 18:27
  • 1
    $\begingroup$ How about how Gaussian elimination is not guaranteed to be stable? (Most matrices are stable under Gaussian elimination in floating point, but there exist matrices which diverge.) $\endgroup$
    – user14717
    Apr 28, 2022 at 18:56
  • 2
    $\begingroup$ @WolfgangBangerth: "Yet it was realized in around 1960 by Wilkinson and others that for certain exceptional matrices, Gaussian elimination is still unstable, even with pivoting" people.maths.ox.ac.uk/trefethen/NAessay.pdf $\endgroup$
    – user14717
    Apr 29, 2022 at 18:40

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.