Results 161 to 170 of about 957 (194)

The Schur Complement of $$\gamma $$-Dominant Matrices

Bulletin of the Iranian Mathematical Society, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lixin Zhou, Zhen-Hua Lyu, Jianzhou Liu
openaire   +2 more sources

Structures Preserved by Schur Complementation

SIAM Journal on Matrix Analysis and Applications, 2006
In this paper we investigate some matrix structures on $\mathbb{C}^{m\times n}$ that are preserved by Schur complementation. The first type of structure is closely related to low displacement rank matrices. Next, we show that for a matrix having a low rank submatrix, the Schur complement also must have a low rank submatrix, which we can explicitly ...
Steven Delvaux, Marc Van Barel
openaire   +1 more source

Matrix Decompositions Involving the Schur Complement

SIAM Journal on Applied Mathematics, 1975
Necessary and sufficient conditions are given for the rank of a sum of matrices over an arbitrary field to equal the sum of the ranks of the matrices. Several decompositions are given of a partitioned matrix into a sum of matrices. These provide a unified treatment of some classical results and some recent results on the ranks and generalized inverses ...
openaire   +3 more sources

Criteria and Schur complements of H-matrices

Journal of Applied Mathematics and Computing, 2009
A complex \(n\times n\) matrix \(A\) is called strictly diagonally (row) dominant if for each \(i= i,\dots,n\) the modulus of the \(i\)th diagonal element of \(A\) exceeds the sum of the moduli of the \(n-1\) off-diagonal elements of the \(i\)th row of \(A\), and \(A\) is called strictly generalized diagonally (row) dominant if there exists a diagonal ...
Liu, Jianzhou, Zhang, Fuzhen
openaire   +2 more sources

Generalized Inverse Formulas Using the Schur Complement

SIAM Journal on Applied Mathematics, 1974
A formula for various generalized inverses of a partitioned complex matrix is established under certain general conditions. The use of this formula in obtaining the Moore–Penrose inverse of an arbitrary complex matrix is discussed.
Burns, Fennell, Carlson, David, Haynsworth, Emilie, Markham, Thomas   +3 more
openaire   +1 more source

General H-matrices and their Schur complements

Frontiers of Mathematics in China, 2014
This paper presents an extensive fully theoretical study of properties of generalized \(H\)-matrices. It is known, that \(H\)-matrices can be divided into three disjoint sets -- the invertible class \(H^I\), the singular class \(H^S\) and the mixed class \(H^M\).
Zhang, Cheng-Yi, Xu, Fengmin, Xu, Zongben, Li, Jicheng   +3 more
openaire   +2 more sources

Schur Complements and Applications

2011
Schur complements arise naturally in the process of inverting block matrices of the form $$M=\left (\begin{array}{cc} A&B\\ C &D\end{array} \right )\!$$ and in characterizing when symmetric versions of these matrices are positive definite or positive semidefinite.
openaire   +1 more source

Systolic array for schur complement computation

International Journal of Computer Mathematics, 1993
The computation of the Schur complement in the domain decomposition method often forms a bottleneck to the problem of solving the large sparse linear systems which occur in the Finite Element Method. A systolic array with ns + n(n + 1)/2 processing elements is designed to compute the Schur complement for a bordered block diagonal matrix.
D. J. Evans, C. R. Wan
openaire   +1 more source

Schur complement preconditioners for anisotropic problems

IMA Journal of Numerical Analysis, 1999
The authors present two new variants of Schur complement domain decomposition preconditioners for 2D anisotropic problems. These new preconditioners are variants of probing method of \textit{T. F. Chan} and \textit{T. P. Mathew} [SIAM J. Matrix Anal. Appl. 13, No. 1, 212-238 (1992; Zbl 0754.65099)]. Probing is a technique which creates a band matrix to
Giraud, Luc, Tuminaro, Ray S.
openaire   +2 more sources

On schur complements in an ep matrix

Periodica Mathematica Hungarica, 1985
Necessary and sufficient conditions are derived for the general EP partitioned matrix to have a Schur complement as EP matrix, too. A decomposition of the partitioned matrix into a sum of EP matrices is given.
openaire   +1 more source