Additive preconditioning and aggregation in matrix computations

Multiplicative preconditioning is a popular tool for handling linear systems of equations provided the relevant information about the associated singular values is available. We propose using additive preconditioners, which are readily available for both general and structured ill conditioned input matrices and which preserve matrix structure. We introduce primal and dual additive preconditioning and combine it with two aggregation techniques. Our extensive analysis and numerical experiments show the efficiency of the resulting numerical algorithms for solving linear systems of equations and some other fundamental matrix computations. Our study provides some new insights into preconditioning, links it to various related subjects of matrix computations, and leads to some results of independent interest. ∗Supported by PSC CUNY Awards 66437-0035 and 67297-0036