TR-2007003: Additive Preconditioning for Matrix Computations

Multiplicative preconditioning is a popular SVD-based techniques for the solution of linear systems of equations. Our novel SVD-free additive preconditioners are more readily available and better preserve matrix structure. We study their generation and their affect on conditioning of the input matrix. In other papers we combine additive preconditioning with aggregation and other relevant techniques to facilitate the solution of linear systems of equations and other fundamental matrix computations. Our analysis and experiments show the power of our algorithms, guide us in selecting most effective policies of preconditioning and aggregation, and provide some new insights into these and related subjects.