Results 11 to 20 of about 408 (148)
Perturbation Bound of the Group Inverse and the Generalized Schur Complement in Banach Algebra [PDF]
Abstract and Applied Analysis, 2012 We investigate the relative perturbation bound of the group inverse and also consider the perturbation bound of the generalized Schur complement in a Banach algebra.
Xiaoji Liu, Yonghui Qin, Hui Wei
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Schur complement of general H‐matrices [PDF]
Numerical Linear Algebra with Applications, 2009 AbstractIt is well known that the Schur complement of some H‐matrices is an H‐matrix. In this paper, the Schur complement of any general H‐matrix is studied. In particular, it is proved that the Schur complement, if it exists, is an H‐matrix and the class to which the Schur complement belongs is studied.
Rafael Bru +3 more
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Operators on anti-dual pairs: Generalized Schur complement
Linear Algebra and its Applications, 2021 15 ...
Zsigmond Tarcsay, Tamás Titkos
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Generalized Schur complements and P-complementable operators
Linear Algebra and its Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Massey, Pedro Gustavo +1 more
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A Power Schur Complement Low-Rank Correction Preconditioner for General Sparse Linear Systems [PDF]
SIAM Journal on Matrix Analysis and Applications, 2021 An effective power based parallel preconditioner is proposed for general large sparse linear systems. The preconditioner combines a power series expansion method with some low-rank correction techniques, where the Sherman-Morrison-Woodbury formula is utilized. A matrix splitting of the Schur complement is proposed to expand the power series. The number
Qingqing Zheng, Yuanzhe Xi, Yousef Saad
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Six generalized Schur complements
Linear Algebra and its Applications, 1988 The authors give a unified treatment of equivalence between some old and new generalizations of the Schur complement of matrices.
Butler, C.A., Morley, T.D.
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Generalized Schur complements of matrices and compound matrices [PDF]
The Electronic Journal of Linear Algebra, 2010 In this paper, we obtain some formulas for compound matrices of generalized Schur complements of matrices. Further, we give some Lowner partial orders for compound matrices of Schur complements of positive semidefinite Hermitian matrices, and obtain some estimates for eigenvalues of Schur complements of sums of positive semidefinite Hermitian matrices.
Jianzhou Liu, Rong Huang
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The Forward Order Law for Least Squareg-Inverse of Multiple Matrix Products
Mathematics, 2019 The generalized inverse has many important applications in the aspects of the theoretic research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the forward order laws ...
Zhiping Xiong, Zhongshan Liu
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Some inequalities on generalized Schur complements
Linear Algebra and its Applications, 1999 Let \(A=[A_{ij}]\) denote a block matrix of order two with square diagonal blocks. The generalized Schur complement \(S_1(A)\) of \(A_{11}\) is defined by \(S_1(A)=A_{22} -A_{21}A^+_{11} A_{12}\) where \(A^+_{11}\) denotes the Moore-Penrose pseudoinverse of \(A_{11}\) so that \(S_1(A)\) is defined also for singular matrices. For a Hermitian matrix \(A\)
Wang, Bo-Ying +2 more
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Generalized Schur complements and oblique projections
Linear Algebra and its Applications, 2002 Let \(A\in L(\mathcal{H})\) be a positive operator, and \(\varphi\) be a closed subspace of the Hilbert space \(\mathcal{H}\). The shorted operator of \(A\) by \(\varphi\) is defined by \(A_{/\varphi}=\max\{X\in L(\mathcal{H})\;:\;0\leq X\leq A \text{ and } R(X)\subseteq \varphi^{\perp}\} \). A pair \((A,\varphi)\) is called compatible if the set \(\{Q\
Corach, Gustavo +2 more
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