We present some new representations for the generalized Drazin inverse of a block matrix with generalized Schur complement being generalized Drazin invertible in a Banach algebra under conditions weaker than those used in recent papers on the subject.

A Schur complement formulation that utilizes a linear iterative solver is derived to solve a free-boundary, Stefan problem describing steady-state solidification via the Isotherm–Newton approach, which employs Newton’s method to simultaneously and efficiently solve for both interface and field equations. This formulation is tested alongside more traditional solution strategies that employ direc...

Extending the corresponding notion for matrices or bounded linear operators on a Hilbert space we define a generalized Schur complement for a non-negative linear operator mapping a linear space into its dual and derive some of its properties.

Abstract For an irreducible and nonpositive matrix, we present the concepts of Perron complement matrix generalized matrix. An inequality that relates matrices inverse N 0 -matrices is derived. In addition, obtain quotient formula based on for Schur complements.

‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized...

In this paper, we investigate EP modular operator matrices on Hilbert C*-modules setting. The necessary and sufficient conditions for some to be are discussed, based the generalized Schur complement. These enable us generalize results of Meenakshi (1958) [11] block matrices.

This paper presents some inequalities on generalized Schur complements. Let A be an n n (Hermitian) positive semide®nite matrix. Denote by A=a the generalized Schur complement of a principal submatrix indexed by a set a in A. Let A‡ be the Moore± Penrose inverse of A and k…A† be the eigenvalue vector of A. The main results of this paper are: 1. k…A‡…a0††P k……A=a†‡†, where a0 is the complement o...

In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems, proving a nonlocal Poincaré inequality. To determine the conditioning of the discretized operator, we prove a spectral equivalence which leads to a mesh size ...

Extensions of the Schur complement and the principal pivot transform, where the usual inverses are replaced by the Moore-Penrose inverse, are revisited. These are called the pseudo Schur complement and the pseudo principal pivot transform, respectively. First, a generalization of the characterization of a block matrix to be an M -matrix is extended to the nonnegativity of the Moore-Penrose inve...