Seminar Announcement

Tensor Methods for Solving Large-scale Systems of Nonlinear Equations

Brett W. Bader and Prof. Robert B. Schnabel
Univ. Colorado, Boulder

Tuesday, June 4, 2002
Bldg. 921, Room 137
10:00 a.m. - 11:00 a.m.

This talk will present an iterative, Krylov-subspace based approach to solving large-scale systems of nonlinear equations using tensor methods. Tensor methods are a class of methods that base each iteration on a model that augments the standard linear models with a limited second-order term. Standard tensor methods for solving small, dense systems of nonlinear equations have performed especially well on problems where the Jacobian matrix is rank deficient or ill-conditioned at the solution. This success originates from the special, restricted form of the quadratic term included in the local tensor model that provides information lacking in a (near) singular Jacobian. This talk will present two variants of an iterative tensor method for solving large-scale systems of nonlinear equations. A third method by Feng and Pulliam will also be included for comparison. These three iterative methods are all based on Krylov subspace projection techniques and intend to capitalize on the success of direct tensor methods, even when only approximately solving the local model. The proposed tensor-Krylov methods require hardly more storage or arithmetic per iteration than a Newton-Krylov method yet still exhibit the superlinear convergence behavior of traditional tensor methods on certain ill-conditioned and singular systems. The ability of the proposed methods to solve the local tensor model to a specified accuracy with very little extra arithmetic beyond standard GMRES is an advantage over existing methods. Preliminary numerical results show promise that these methods will outperform Newton-GMRES on certain problems.

This seminar is hosted by the Computational Sciences and Mathematics Research Department at Sandia National Labs in Livermore, CA. For more information on this or other events, visit http://csmr.ca.sandia.gov/news.html. Visitors from outside Sandia require advance arrangements in order to attend. For more information, please contact the CSMR office management assistant Doretha Smith at dahall@sandia.gov or (925) 294-4630.