We propose a saddle-point preconditioner for an optimization problem constrained by the time-dependent Stokes equations, discretized using backward Euler method in time. The key ingredients are inner iteration (1, 1)-block, accelerated known heat control problem, and approximation of Schur complement involving commutator argument applied to block matrix. Numerical results demonstrate efficacy r...

This article reviews and discusses a geometric perspective on the well-known fact in graph theory that effective resistance is metric nodes of graph. The classical proofs this make use ideas from electrical circuits or random walks; here we describe an alternative approach which combines (using simplices) algebraic Schur complement) ideas. These perspectives are unified matrix identity Miroslav...

This paper presents a Domain Decomposition-type method for solving real symmetric (or Hermitian complex) eigenvalue problems in which we seek all eigenpairs in an interval [α, β], or a few eigenpairs next to a given real shift ζ. A Newton-based scheme is described whereby the problem is converted to one that deals with the interface nodes of the computational domain. This approach relies on the...

In this article, we consider some representations of {1, 3}, {1, 4}, {1, 2, 3} and {1, 2, 4}-inverses of a partitioned matrix M which are equivalent to some rank additivity conditions. We present some applications of these results to generalizations of the Sherman-Morrison-Woodbury-type formulae.

We consider the problem of dynamically maintaining (approximate) all-pairs effective resistances in separable graphs, which are those that contain small balanced separators. We give a fully dynamic algorithm that maintains (1 + ε)-approximations of the all-pairs effective resistances of an n-vertex graph G undergoing edge insertions and deletions with Õ( √ n/ε) worst-case update time and Õ( √ n...

This paper presents a preconditioner based on solving approximate Schur complement systems with overlapping restricted additive Schwarz methods (RAS). The construction of the preconditoner, called SchurRAS, is as simple as in the standard RAS. The communication requirements for each application of the preconditioning operation are similar with those of the standard RAS approach. In the particul...