We consider an algebraic multilevel preconditioning method for SPD matrices resulting from finite element discretization of elliptic PDEs. In particular, we focus on non-M matrices. The method is based on element agglomeration and assumes access to the individual element matrices. The coarse-grid element matrices are simply Schur complements computed from local neighborhood matrices (agglomerat...

General properties of global covariance matrices representing bipartite Gaussian states can be decomposed into properties of local covariance matrices and their Schur complements. We demonstrate that given a bipartite Gaussian state ρ12 described by a 4 × 4 covariance matrix V, the Schur complement of a local covariance submatrix V1 of it can be interpreted as a new covariance matrix representi...

We address the problem of blind multichannel identification in a communication context. Using a deterministic model for the input symbols and only second order statistics, we develop a simple algorithm, based on the Generalized Schur algorithm to apply LDU decomposition of the covariance matrix of the received data. We show that this method leads to identification of the channel, up to a consta...

We study two different decomposition algorithms for the general (nonconvex) partially separable nonlinear program (PSP): bilevel decomposition algorithms (BDAs) and Schur interior-point methods (SIPMs). BDAs solve the problem by breaking it into a master problem and a set of independent subproblems, forming a type of bilevel program. SIPMs, on the other hand, apply an interior-point technique t...

The discretization of Cahn-Hilliard equation with obstacle potential leads to a block 2ˆ2 non-linear system, where the p1, 1q block has a non-linear and non-smooth term. Recently a globally convergent Newton Schur method was proposed for the non-linear Schur complement corresponding to this non-linear system. The solver may be seen as an inexact Uzawa method which has the falvour of an active s...