On A Recursive Schur Preconditioner For Iterative Solution Of A Class Of Dense Matrix Problems

There are currently several distinct preconditioning methods for dense matrices based on applying a wavelet transform to obtain a matrix with a large number of small entries. A sparse preconditioner for this transformed matrix can be formed by setting to zero entries that are assumed to be unimportant. The effectiveness of the preconditioner depends on retaining the most important entries and on ensuring that they are positioned conveniently within the transformed matrix. In this paper we present a new, recursive preconditioning strategy that takes into account more of the significant entries without greatly increasing cost and outperforms existing methods in certain cases.

Keywords:

• Schur Complement
• Gmres
• Dwt
• Dense Matrices