We give explicit representations of the generalized Drazin inverse of a block matrix having generalized Schur complement generalized Drazin invertible in Banach algebras. Also we give equivalent conditions under which the group inverse of a block matrix exists and a formula for its computation. The provided results extend earlier works given in the literature. 2010 Mathematics Subject Classific...

If a nonnegative selfadjoint linear relation A in Hilbert space and closed subspace S are assumed to satisfy that the domain of is invariant under orthogonal projector onto S, then admits particular matrix representation with respect decomposition S⊕S⊥. This used give explicit formulae for Schur complement on as well S-compression A.

We introduce new expressions for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra under some conditions. We generalized some recent results for Drazin inverse and group inverse of complex matrices.

In this paper, we give a new additive formula for the Drazin inverse under conditions weaker than those used in some current literature on this subject. Also, we obtain representations for the Drazin inverse of a complex block matrix having generalized Schur complement equal to zero. 2000 Mathematics Subject Classification: 15A09

To our knowledge, most numerical methods for solving discretizations of the Stokes equations depend on the Schur complement and thus the convergence rate depends on the aspect ratio of the domain. We present a preconditioner for a staggered grid discretization of the Stokes equations which is proven to be independent of the aspect ratio. Finally numerical experiments confirm the robustness of t...

Abstract—In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of such system are obtained by solving a set of Linear Matrix Inequalities (LMIs). One numerical example is included to show the effectiveness ...

The focus of this paper is a penalty-based strategy for preconditioning elliptic saddle point systems. As the starting point, we consider the regularization approach of Axelsson in which a related linear system, differing only in the (2,2) block of the coefficient matrix, is introduced. By choosing this block to be negative definite, the dual unknowns of the related system can be eliminated res...