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Schur complements in Krein spaces [PDF]
Integral Equations and Operator Theory, 2007 The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded) J-selfadjoint operator A (with the unique factorization property) acting on a Krein space H and a suitable closed subspace S ...
Maestripieri, Alejandra Laura +1 more
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Manifestations of the Schur complement
Linear Algebra and its Applications, 1974 AbstractThis expository paper describes the ways in which a matrix theoretic construct called the Schur complement arises. Properties of the Schur complement are shown to have use in computing inertias of matrices, covariance matrices of conditional distributions, and other information of interest.
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Hypocoercivity with Schur complements
Annales Henri Lebesgue, 2022 We propose an approach to obtaining explicit estimates on the resolvent of hypocoercive operators by using Schur complements, rather than from an exponential decay of the evolution semigroup combined with a time integral. We present applications to Langevin-like dynamics and Fokker–Planck equations, as well as the linear Boltzmann equation (which is ...
Bernard, Etienne +3 more
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Non-Overlapping Domain Decomposition via BURA Preconditioning of the Schur Complement
Mathematics, 2022 A new class of high-performance preconditioned iterative solution methods for large-scale finite element method (FEM) elliptic systems is proposed and analyzed.
Nikola Kosturski +2 more
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The Pauli Problem for Gaussian Quantum States: Geometric Interpretation
Mathematics, 2021 We solve the Pauli tomography problem for Gaussian signals using the notion of Schur complement. We relate our results and method to a notion from convex geometry, polar duality.
Maurice A. de Gosson
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Open Mathematics, 2015 The theory of Schur complement plays an important role in many fields, such as matrix theory and control theory. In this paper, applying the properties of Schur complement, some new estimates of diagonally dominant degree on the Schur complement of I(II)-
Wang Feng, Sun Deshu
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A Finite Element-Based Characteristic Mode Analysis
IEEE Open Journal of Antennas and Propagation, 2022 A novel Green’s function-free characteristic modes formulation is introduced in this work. The desired impedance or admittance matrix is obtained utilizing and appropriately modifying the versatile finite element method.
Konstantinos D. Paschaloudis +3 more
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Complementary Schur complements
Linear Algebra and its Applications, 1994 Let \(M\) and \(N\) be \(m\times m\) and \(n\times n\) complex matrices, respectively. The authors define \(M\) and \(N\) to be ``Schur coupled'' if there exist matrices \(A,B,C\) and \(D\) such that \(M=D-CA^{-1}B\) and \(N=A- BD^{-1}C\). The main result of this paper is that the following are equivalent: (i) \(M\) and \(N\) are Schur coupled; (ii ...
Bart, Harm, Tsekanovskii, VE
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A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems
Mathematics, 2023 In this paper, a new preconditioning method is proposed for the linear system arising from the elliptic optimal control problem. It is based on row permutations of the linear system and approximations of the corresponding Schur complement inspired by the
Chaojie Wang, Jie Chen, Shuen Sun
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A preconditioner for the Schur complement matrix [PDF]
, 2006 A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a global problem in a narrow strip around the interface.
Dalcin, Lisandro Daniel +5 more
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