Results 141 to 150 of about 12,740 (173)

Some generalized inverses of partition matrix and quotient identity of generalized Schur complement

Applied Mathematics and Computation, 2008
The authors initially extend the notion of the generalized Schur complement and study the expression of the Moore-Penrose inverse of \(2\times 2\) block matrices. Then, they propose expressions of the group inverse and the Drazin inverse for a block matrix under some conditions.
Sheng, Xingping, Chen, Guoliang
openaire   +2 more sources

On the Drazin inverse of block matrices and generalized Schur complement

Applied Mathematics and Computation, 2009
Different expressions are well-known for the Banaksiewicz-Schur form of a matrix involving the Moore-Penrose inverse, the group inverse or the Drazin inverse. In all of these cases, the generalized Schur complement (considering the corresponding Moore-Penrose, group or Drazin block) plays an important role.
Martínez-Serrano, M. F., Castro-González, N.   +1 more
openaire   +2 more sources

A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse

SIAM Journal on Applied Mathematics, 1974
Suppose the complex matrix M is partitioned into a $2 \times 2$ array of blocks; let $M_{11} = A,M_{12} = B,M_{21} = C,M_{22} = D$. The generalized Schur complement of A in M is defined to be $M/A = D - CA^ + B$, where $A^ + $ is the Moore–Penrose inverse of A. The relationship of the ranks of M, A, and $M/A$ is determined.
Carlson, David, Haynsworth, Emilie, Markham, Thomas   +2 more
openaire   +1 more source

Perturbation analysis for the generalized Schur complement of a positive semi‐definite matrix

Numerical Linear Algebra with Applications, 2007
AbstractLet and S=C−BHA†B be the generalized Schur complement of A⩾0 in P. In this paper, some perturbation bounds of S are presented which generalize the result of Stewart (Technical Report TR‐95‐38, University of Maryland, 1995) and enrich the perturbation theory for the Schur complement. Also, an error estimate for the smallest perturbation of C,
Wei, Musheng, Wang, Minghui
openaire   +1 more source

Approximate Schur Complement Multilevel Methods for General Sparse Systems

2000
We introduce a multilevel preconditioner based on an approximate Schur complement using sparse approximate inverses. We give a brief introduction to the algorithm followed by some results for two-dimensional and three-dimensional model problems.
Benzi, Michele, DeLong, Michael
openaire   +1 more source

On the generalized Drazin inverse in Banach algebras in terms of the generalized Schur complement

Applied Mathematics and Computation, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Robles, J., Martínez-Serrano, M. F., Dopazo, E.   +2 more
openaire   +1 more source

The generalized Schur complement in group inverses and (k + 1)-potent matrices

Linear and Multilinear Algebra, 2006
In this article, two facts related to the generalized Schur complement are studied. The first one is to find necessary and sufficient conditions to characterize when the group inverse of a partitioned matrix can be expressed in the Schur form. The other one is to develop a formula for any power of the generalized Schur complement of an idempotent ...
Julio Benítez, Néstor Thome
openaire   +1 more source

Spectral analysis of coupled PDEs and of their Schur complements via Generalized Locally Toeplitz sequences in 2D

Computer Methods in Applied Mechanics and Engineering, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dorostkar, A., Neytcheva, M., SERRA CAPIZZANO, STEFANO   +2 more
openaire   +3 more sources

The group invertibility of a matrix with nonsingular generalized Schur complement

Publicationes Mathematicae Debrecen
We present the group invertibility of a complex matrix under new perturbed conditions. The group invertibility for a block matrix with nonsingular generalized Schur complement is thereby obtained.
Huanyin Chen, Marjan Sheibani
openaire   +2 more sources

On generalized Schur complement of matrices and its applications to real and integer matrix factorizations

2022
Summary: We provide a general finite iterative approach for constructing factorizations of a matrix \(A\) under a common framework of a general decomposition \(A=BC\) based on the generalized Schur complement. The approach applies a zeroing process using two index sets.
openaire   +2 more sources