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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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Inner Formulation of Lyapunov Stability Test and Generalized Schur-Complement
IFAC Postprint Volumes IPPV / International Federation of Automatic Control, 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 ...
E I Jury, O Huseyin
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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.
Xiaoji Liu +2 more
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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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Perturbation analysis for the generalized Schur complement of a positive semi‐definite matrix
Numerical Linear Algebra with Applications, 2007AbstractLet 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,
Musheng Wei, Minghui Wang
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Applied Mathematics and Computation, 2009
Starting with I. Schur there is a considerable literature describing conditions on the blocks of a \(2\times2\) block matrix which enable us to give a simple expression for the inverse matrix, or more generally the Drazin inverse or Moore-Penrose (MP) inverse [see, for example, \textit{X. Sheng} and \textit{C. Chen}, Appl. Math. Comput. 196, No.~1, 174-
Dragana S Cvetković Ilić
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Starting with I. Schur there is a considerable literature describing conditions on the blocks of a \(2\times2\) block matrix which enable us to give a simple expression for the inverse matrix, or more generally the Drazin inverse or Moore-Penrose (MP) inverse [see, for example, \textit{X. Sheng} and \textit{C. Chen}, Appl. Math. Comput. 196, No.~1, 174-
Dragana S Cvetković Ilić
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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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The group invertibility of a matrix with nonsingular generalized Schur complement
Publicationes Mathematicae DebrecenWe 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
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Approximate Schur Complement Multilevel Methods for General Sparse Systems
2000We 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
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Computer Methods in Applied Mechanics and Engineering, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dorostkar, A. +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dorostkar, A. +2 more
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