A new approach to algebraic multilevel methods using sparse approximate

A new approach to algebraic multilevel methods will be presented. The appoach is based on the observation that sparse approximate inverses typically approximate quite well on a large subspace, but they do not perform that well on the whole space. A natural consequence is to augment the sparse approximate inverse with correction term of smaller rank. This approach leads to an algebraic multilevel method. We will present techniques for the construction of the correction term. An essential part will be an approximate QR decomposition which is used to detect certain columns of the residual matrix. These columns will be used for the correction term.