By Topic

Improving the speed of convergence of GMRES for certain perturbed tridiagonal systems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Huy Nguyen ; Department of Mathematics, Baylor University, Waco, TX 76798 ; Matthew A. Beauregard ; Ron Morgan

Numerical approximations of partial differential equations often require the employment of spatial adaptation or the utilization of non-uniform grids to resolve fine details of the solution. While the governing continuous linear operator may be symmetric, the discretized version may lose this essential property as a result of adaptation or utilization of non-uniform grids. Commonly, the matrices can be viewed as a perturbation to a known matrix or to a previous iterate's matrix. In either case, a linear solver is deployed to solve the resulting linear system. Iterative methods provide a plausible and affordable way of completing this task and Krylov subspace methods, such as GMRES, are quite popular. Upon updating the matrices as a result of adaptation or multi-grid methodologies, approximate eigenvector information is known stemming from the prior GMRES iterative method. Hence, this information can be utilized to improve the convergence rate of the subsequent iterative method. A one dimensional Poisson problem is examined to illustrate this methodology while showing notable and quantifiable improvements over standard methods, such as GMRES-DR.

Published in:

System Theory (SSST), 2013 45th Southeastern Symposium on

Date of Conference:

11-11 March 2013