Preconditioning Techniques for Linear Systems of Equations

Texas A&M Engineering Experiment Station, College Station TX

Investigators

Abstract

NSF Proposal Number: 0431068 Title: Preconditioning techniques for linear systems of equations PI: Vivek Sarin, Dept. of Computer Science, Texas A&M University Abstract: The solution of linear systems of equations is a fundamental problem that must be tackled in various areas of science and engineering. Iterative methods are used to solve large sparse systems from partial differential equations as well as large dense systems from integral equations. Preconditioning techniques are necessary to accelerate the rate of convergence of these solvers. An ideal preconditioner should be robust, effective, parallelizable, and inexpensive to compute and apply to the linear system. When solving dense systems, the unavailability of the coefficient matrix often limits the choice of preconditioners. The goal of the project is to develop novel preconditioning techniques for sparse and dense linear systems. These techniques will use a sequence of linear transformations to obtain a preconditioned system from the original one. Techniques will be developed to analyze the preconditioned system, and schemes will be developed to improve the effectiveness of the preconditioner. The resulting preconditioners will be robust, effective, and inexpensive. These preconditioning techniques will be implemented, analyzed, and tested on a variety of problems. These efforts will be integrated with interdisciplinary collaborative research activities to ensure a greater impact on application areas.