Re: Suggestions for hardware implementation

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Ulrich Kulisch schrieb:
> Please have a look at the Kirchner/Kulisch paper. I attach a copy

This is interesting but does not yet address the use of the
pipelines for both interval arithmetic and real directed operations.

Note that many of the more advanced kinds of rigorous computations
require a mix of interval computation and real computation with
directed rounding. Thus the directed rounding pipelines should be
usable for both kinds of operations.

I had mentioned already
- the Hansen-Bliek method for solving linear systems with
  interval coefficients
  Reliable Computing 5 (1999), 131-136.
  Erratum, Reliable Computing 6 (2000), 227.
  http://www.mat.univie.ac.at/~neum/papers.html#ning
- Barth and Nuding's optimal solution of linear systems with
  an interval M-matrix
  Computing 12 (1974), 117-125
- the linear interpolation algorithms in Section 5.8 of
  ViennaProposal-v3.0
but there are further cases including
- optimal aposteriori bounds in linear progrsmming
  A. Neumaier and O. Shcherbina,
  Safe bounds in linear and mixed-integer programming,
  Math. Programming A 99 (2004), 283-296.
  http://www.mat.univie.ac.at/~neum/papers.html#mip
- Makino's range reduction technique; see Theorem 9.1 in
  A. Neumaier,
  Taylor forms - use and limits,
  Reliable Computing 9 (2002), 43-79.
  http://www.mat.univie.ac.at/~neum/papers.html#taylor

I'd be interested in additional pointers for such mixed
interval/directed rounding calculations.


Arnold Neumaier