Wednesday, July 16

3:15 PM-5:15 PM
Building 200, Room 2

Preconditioning with Incomplete Factorizations

Efficient incomplete matrix factorizations provide relatively inexpensive ways to approximate the inverses of matrices. They can be used as preconditioners for accelerating convergence rates of iterative methods for solving large sparse systems of linear equations, which arise in a large variety of scientific and engineering applications. Speakers in this minisymposium will discuss recent work on developing robust and efficient algorithms for incomplete matrix factorizations.

Preconditioners accelerate the convergence of iterative methods. Typically, preconditioners use polynomials, incomplete factors, or approximate inverses. Polynomial preconditioners require estimates of a few eigenvalues of the matrix and are useful in applications where such eigenvalue information is known or easily computed. Incomplete factorization based preconditioners are general purpose and robust; however, applying such preconditioners in parallel can be inefficient. Approximate inverse preconditioners typically do not accelerate convergence as well as incomplete factorization preconditioners but they can be applied efficiently on parallel multiprocessors.

The minisymposium will focus on new advances in developing preconditioners based on incomplete factorizations. Some of the speakers will discuss the exploitation of symbolic factorization techniques from sparse direct methods in the construction of incomplete factors.

Organizers: Esmond G. Ng, Oak Ridge National Laboratory; and Padma Raghavan, The University of Tennessee, Knoxville

3:15 Improved Preconditioning Techniques for Indefinite Matrices
E. Chow and Yousef Saad, University of Minnesota, Minneapolis
3:45 Multi-Level One-Way Dissection Preconditioner for Unsteady Incompressible Navier-Stokes Equation
Alan George, Wei-Pai Tang, and Ya Dan Wu, University of Waterloo, Canada
4:15 A Combinatorial Approach to Preconditioners for Iterative System Solvers
Keith Gremban and Gary Miller, Carnegie Mellon University
4:45 Exploiting Sparse Direct Techniques in Constructing Incomplete Factorizations
John R. Gilbert, Xerox Palo Alto Research Center; Esmond G. Ng, Organizer; and Barry W. Peyton, Oak Ridge National Laboratory; and Padma Raghavan, University of Tennessee

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