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         Tel Aviv University
  School of Mathematical Sciences
    Applied Mathematics Seminar
 
((There will also be an additional special seminar on Thursday.
It will be announced separately.))
 
Date:          Tuesday May 31, 2011, 15:10
Place:             Schreiber Bldg, Room 309
 
Speaker:     Vladimir Rochlin, Yale University
 
Title: Accurate Randomized Algorithms of Numerical Analysis
 
Abstract:
Randomized algorithms are ubiqutous in computer science and computer
engineering. Many problems that are intractable when viewed
deterministically can be effectively solved with probabilistic
techniques. Perhaps the most important aspect of most randomized
procedures in current use is the fact that they produce the correct
result with (practically speaking) 100% reliability, and with
(essentially) machine precision.
 
Historically, randomized techniques have been less popular in numerical
analysis. Most of them trade accuracy for speed, and in many numerical
environments one does not want to add yet another source of inaccuracy
to the calculation that is already sufficiently inaccurate. One could
say that in numerical analysis probabilistic methods are an approach of
last resort.
 
I will discuss several probabilistic algorithms of numerical linear
algebra that are never less accurate than their deterministic
counterparts, and in fact tend to produce better accuracy. In many
situations, the new schemes have lower CPU time requirements than
existing methods, both asymptotically and in terms of actual timings. I
will illustrate the approach with several numerical examples, and
discuss possible extensions.
 
______________________________________________________________________
 
Dr. Adi Ditkowski                                                     |
Department of Applied Mathematics                                     |
School of Mathematical Sciences          phone:  972-3-640-5987       |
Tel Aviv University,                     fax  :  972-3-640-9357       |
Tel Aviv, 69978 Israel                   email:   <adid@post.tau.ac.il>  |
______________________________________________________________________
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Adi Ditkowski   <adid@post.tau.ac.il>