[BANANA] LA/Opt seminars TODAY (Marielba Rojas and Martin van Gijzen)

[Michael A. Saunders]

Reminder: Two matrix-computation talks today (and one on Friday)

   4:15pm today  Marielba Rojas (DTU and Delft)
                 Accelerating the LSTRS Algorithm

   4:45pm today  Martin van Gijzen (Delft)
                 IDR(s): a family of simple and fast methods
                 for solving large nonsymmetric linear systems

   4:15pm Friday Martin Stoll (Oxford)
                 Preconditioning for PDE-constrained optimization

Three abstracts follow.

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

    4:15pm Wed Oct 21, 2009
    Terman 332

    FIRST OF TWO 30-min TALKS TODAY

    Dr Marielba Rojas
    Technical University of Denmark (DTU)
    and Delft University of Technology, The Netherlands
    http://www2.imm.dtu.dk/~mr/

    Accelerating the LSTRS Algorithm

The LSTRS algorithm presented in

    M. Rojas, S.A. Santos, and D.C. Sorensen.
    A new matrix-free method for the large-scale trust-region subproblem,
    SIAM J. Optim. 11(3): 611-646, 2000

is an iterative procedure designed for solving large-scale quadratic
problems with one norm constraint, or trust-region subproblems.  The
method is based on a reformulation of the trust-region subproblem as a
parameterized eigenvalue problem.  The main computation in LSTRS is the
solution of a large symmetric eigenvalue problem at each step.

The associated software

    M. Rojas, S.A. Santos, and D.C. Sorensen.
    Algorithm 873: LSTRS: MATLAB software for large-scale trust-region
    subproblems and regularization, ACM Trans. Math. Software 34(2), 2008

offers several possibilities for the solution of the eigenproblems.
We will present a brief description of the LSTRS algorithm with focus
on the eigenvalue problems and their features.  We describe recent
work on improving the performance of LSTRS through more efficient
eigenvalue computations.

This is joint work with Joerg Lampe, Danny Sorensen, and Heinrich Voss.

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

    4:45pm Wed Oct 21, 2009
    Terman 332

    SECOND OF TWO 30-min TALKS TODAY

    Dr Martin van Gijzen
    Delft University of Technology, The Netherlands
    http://ta.twi.tudelft.nl/nw/users/gijzen/

    IDR(s): a family of simple and fast methods for solving
    large nonsymmetric linear systems

The IDR method was proposed in 1980 by Sonneveld as an iterative
method for solving nonsymmetric systems of equations.  For a long time
the method was forgotten, except by the few who remembered IDR as the
direct predecessor of CGS and Bi-CGSTAB.

Recently we have reconsidered IDR and generalized it to IDR(s).
Extensive experiments show an excellent performance: for important
classes of problems IDR(s) is considerably faster than other short
recurrence methods such as Bi-CGSTAB and Bi-CGSTAB(l).

In the talk we will outline the ideas behind IDR(s).  We will discuss
some recent developments and present extensive experimental results
from different applications (ocean circulation, sound propagation in
the earth crust).  We will illustrate the parallel performance of the
method with experiments on the Dutch DAS3 grid computer, which
consists of five geographically separated clusters.

Joint work with Peter Sonneveld.

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

    4:15pm Fri Oct 23, 2009
    Terman 453

    Martin Stoll
    Oxford University Computing Laboratory, UK
    martin.stoll80 at googlemail.com
    http://people.maths.ox.ac.uk/~stoll/

Preconditioning for PDE-constrained optimization

Advances in algorithms and hardware have enabled more research on the
optimization of functions with constraints given by partial
differential equations.  Problems of this type arise in a variety of
applications and pose significant challenges to optimization
algorithms and numerical methods.  In this talk we present
preconditioners for problems in a general setup and also when
additional box constraints are introduced for the control.  These
constraints add an extra layer of complexity to the optimization
method and the efficient solution of the linear system is very
important.

Block-diagonal preconditioners present one possibility to solve the
arising saddle point problems efficiently.  In addition, we discuss
the use of block-triangular preconditioners that can be used in a
non-standard inner product iterative method.  We show that the
drawbacks of this method can be easily overcome by choosing
appropriate preconditioners for the blocks of the saddle point system.
We present an eigenvalue analysis for the preconditioners and
illustrate their competitiveness on some examples.

If time permits we will discuss some recent developments of using
these preconditioners for the solution of Allen-Cahn variational
inequalites.  This is joint work with Andy Wathen and Tyrone Rees.

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