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Distributed Schur Complement Techniques for General Sparse Linear Systems
SIAM Journal on Scientific Computing, 1999Preconditioning techniques for solving general sparse linear systems on distributed memory environments are presented. Two of them are based on an approximate solution process for the global system exploiting approximate LU factorizations for diagonal blocks of the Schur complement, while another uses a sparse approximate-inverse technique to determine
Saad, Yousef, Sosonkina, Maria
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Generalized Inverse Formulas Using the Schur Complement
SIAM Journal on Applied Mathematics, 1974A 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 +3 more
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General H-matrices and their Schur complements
Frontiers of Mathematics in China, 2014This 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 +3 more
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Block idempotent matrices and generalized Schur complement
Applied Mathematics and Computation, 2007Given a matrix partitioned into \(2\times 2\) blocks, where the left upper block is a nonsingular matrix denoted as \(A\). The paper deals with the idempotency of the generalized Schur complement with a generalized inverse \(A^{(2)}_{T,S}\), where \(A^{(2)}_{T,S}\) denotes the {2}-inverse of \(A\) with range \(T\) and null space \(S\).
Zhou, Jinhua, Wang, Guorong
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Generalized inverses of large matrices using the generalized Schur complement
IEEE Proceedings on Southeastcon, 2002The development of a software package for calculating the generalized inverse of a large real matrix is described. A large matrix is defined as a matrix that is too large to reside in computer memory. The computer software is written in Microsoft C v5.0 and can be implemented on an IBM-PC or compatible.
N.I. Frank, I.N. Imam
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Generalized Schur-complements and a test for total positivity
Applied Numerical Mathematics, 1987The classical concept of Schur-complements is generalized and new determinantal identities are given. As an application a new test for totally positive matrices is derived.
Gasca, M., Mühlbach, G.
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Representations of generalized inverses of partitioned matrix involving Schur complement
Applied Mathematics and Computation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xiaoji +2 more
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Generalized Schur Complements Involving the Kronecker Products of Positive Semidefinite Matrices
Mathematical Notes, 2020Schur complements have been extensively studied and their origin can be traced back to Issai Schur. The name was coined by Emilie Virginia Haynsworth for a square nonsingular matrix. An important reference which is a survey in the area is [\textit{F. Zhang} (ed.), The Schur complement and its applications. New York, NY: Springer (2005; Zbl 1075.15002)],
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Inner Formulation of Lyapunov Stability Test and Generalized Schur-Complement
IFAC Proceedings Volumes, 1981Abstract It is shown in this paper that for the stability condition of ẋ = Ax and x k = AX k-1 there exists a positive innerwise matrix, such that Q is a negative semi-innerwise matrix p. The inner formulation is shown for Hermite, reduced Hermite, Schur-Cohn and reduced Schur-Cohn criteria, and other criteria related to root-clustering problems ...
Ö. Hüseyin, E.I. Jury
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