Scientific Computing Seminar

Date:

Thursday, December 2, 2004

Time:

1:00pm-2:00pm

Location:

50A-5132

Seminar Speaker:

Chen Greif
The University of British Columbia
http://www.cs.ubc.ca/~greif/

Title:

An Algebraic Analysis of Augmented Lagrangian Techniques Applied to Saddle-Point Linear Systems

Abstract:

This talk considers the numerical solution of block structured linear systems of the form

[A B] [x] = [c]

[B' 0] [y] [d]

The problem is treated within a general algebraic framework. We focus on cases where the (1,1) block, A, is positive semidefinite, and analyze a technique of augmented Lagrangian, by which the linear system is modified by adding a term of the form B W B' x = B W d to the first block row.
We take an approach of minimizing the condition number of the (1,1) block, and show that it effectively accelerates convergence of Krylov solvers. The spectrum of the matrices and block preconditioning approaches are discussed. We also address the circumstances in which the analysis can be extended to the case of an indefinite (1,1) block, which is of much importance in applications related to nonlinear optimization.

The work presented in this talk is joint with Gene Golub and Jim Varah.

Sponsor of Seminar:

Esmond Ng

Scientific Computing

Contact Esmond G. Ng EGNg@lbl.gov