Additive Preconditioning and Aggregation in Matrix Computations

Multiplicative preconditioning is a popular SVD-based techniques for the solution of linear systems of equations, but our SVD-free additive pre-conditioners are more readily available and better preserve matrix struc-ture. We combine additive preconditioning with aggregation and other relevant techniques to facilitate the solution of linear systems of equations and some other fundamental matrix computations. Our analysis and ex-periments show the power of our approach, guide us in selecting most eective policies of preconditioning and aggregation, and provide some new insights into these and related subjects of matrix computations