[BANANA] LA/Opt seminar Wed April 30 (Sherry Li)

[Michael A. Saunders]

   Linear Algebra and Optimization Seminar (CME510)
   iCME, Stanford University
   http://icme.stanford.edu/seminars/seminars.php

   4:15pm Wed April 30, 2008
   Room GESB 134 (Green Earth Sciences Building)

   Dr Xiaoye Sherry Li
   Computational Research Division, LBNL
   and Computer Science Division, UC Berkeley
   http://crd.lbl.gov/~xiaoye/

Precise Solutions for Linear Systems and Least Squares Problems

We present the algorithms, error bounds, and numerical results of
extra-precise iterative refinement for linear systems and linear least
squares problems.  The algorithms require only limited use of extra
precision and add only O(n^2) work to the O(n^3) cost of LU, or O(m n)
work to the O(m n^2) cost of QR.  Our algorithms reduce the forward
normwise and componentwise errors to O(epsilon) unless the system is
too ill-conditioned.  The extra precision is facilitated by the new
extended-precision BLAS standard in a portable way, and the algorithms
will be included in a future release of (Sca)LAPACK.

Joint work with James Demmel, Yozo Hida, Jason Riedy, and Meghana
Vishvanath of UC Berkeley.