[BANANA] LA/Opt seminar TODAY (Andrew Bradley)

[Michael A. Saunders]

    REMINDER, seminar this afternoon


    Linear Algebra and Optimization Seminar (CME 510)
    iCME, Stanford University
    http://icme.stanford.edu/seminars/seminars.php

    4:15pm Wed May 6, 2009
    Terman 332

    Andrew M. Bradley <ambrad at stanford.edu>
    iCME, Stanford University

    Stochastic Binormalization of Symmetric Matrices

A symmetric matrix A is binormalized if the norm of each row (and
column) is the same.  Many matrices can be binormalized by
symmetric diagonal scaling, and the resulting matrix frequently
has a smaller condition number.  In 2004, Livne and Golub
introduced an algorithm to find such a diagonal scaling matrix D.
The algorithm must access the elements of A individually.  We
first answer three open questions from their paper concerning the
existence and uniqueness of a binormalizing D.  Then we introduce
a stochastic algorithm to find D while accessing A only through
matrix-vector products.  Finally, we introduce a limited-memory
quasi-Newton method that incorporates stochastic binormalization.