Modified Krylov acceleration for parallel environments Original Research Article

This paper considers a few variants of Krylov subspace techniques for solving linear systems on parallel computers. The goal of these variants is to avoid global dot-products which hamper parallelism in this class of methods. They are based on replacing the standard Euclidean inner product with a discrete inner product over polynomials. The set of knots for the discrete inner product is obtained by estimating eigenvalues of the coefficient matrix.