K O L L O Q U I U M
	       
 der Arbeitsgruppe Modellierung, Numerik, Differentialgleichungen



                     A N N O U N C E M E N T
		     

Speaker      :  Prof. Dr. Andrew Knyazev (Denver, Colorado, USA)
                ------------------------
		
Title of talk:  Mathematical and Computer Science Aspects 
                of Eigenvalue Computations
		
Date         :  Tuesday, June 12, 2007
 
Time         :  16:15 Uhr   
 
Room         :  MA 313 (TU Berlin: Strasse des 17. Juni 136) 

invited by   :  Volker Mehrmann

Abstract     :  

The first part of the talk is purely mathematical and concerns bounds on 
the
changes in Ritz value with the change of the trial subspaces in the
Rayleigh-Ritz method. The sketch of the proof will be presented, which
deeply involves angles between subspaces and operator extensions in
Euclidean and Hilbert spaces.

In the second part of the talk, I describe our Block Locally Optimal
Preconditioned Eigenvalue Xolvers (BLOPEX) software package that includes
our  eigenxolver, called the Locally Optimal Block Preconditioned 
Conjugate
Gradient Method. BLOPEX supports parallel computations through an abstract
layer. BLOPEX is incorporated in the HYPRE package from LLNL and is
available as an external block to the PETSc package from ANL as well as a
stand-alone serial library. Hypre and PETSc packages provide high quality
multigrid and domain decomposition preconditioning on parallel clusters 
with
distributed or shared memory architecture.  Scalability results using 
BLOPEX
with Hypre and PETSc on BlueGene/L supercomputer with solving eigenvalue
problems of record sizes are presented.

[1] A. V. Knyazev and M. E. Argentati, Majorization for Changes in Angles
Between Subspaces, Ritz values, and graph Laplacian spectra, SIMAX, 29
(2006), 15-32.
[2] A. V. Knyazev, A. Jujunashvili, and M. E. Argentati, Angles Between
Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and
Alternating Projectors Methods, <A TARGET="_new" 
HREF="http://arxiv.org/abs/0705.1023">http://arxiv.org/abs/0705.1023</A>.
[3] A. V. Knyazev, I. Lashuk, M. E. Argentati, and E. Ovchinnikov, Block
Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and
PETSc, <A TARGET="_new" 
HREF="http://arxiv.org/abs/0705.2626">http://arxiv.org/abs/0705.2626</A>.