Results 11 to 20 of about 957 (194)
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 \({\mathcal{H}}\) and a suitable closed subspace \({\mathcal{S}}\) of \({\mathcal{H}}\), the Schur complement \(A_{/[\mathcal{S}]}\) of ...
Maestripieri, Alejandra Laura +1 more
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Linear Algebra and its Applications, 1979 AbstractLet A be an n×n complex matrix. For a suitable subspace M of Cn the Schur compression A M and the (generalized) Schur complement A/M are defined. If A is written in the form A= BCST according to the decomposition Cn=M⊕M⊥ and if B is invertible, then AM=BCSSB−1C and A/M=000T−SB−1C· The commutativity rule for Schur complements is proved: (A/M)/N=(
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Schur complements and statistics
Linear Algebra and its Applications, 1981 AbstractIn this paper we discuss various properties of matrices of the type S=H−GE−1F, which we call the Schur complement of E in A = EFGH The matrix E is assumed to be nonsingular. When E is singular or rectangular we consider the generalized Schur complements S=H−GE−F, where E− is a generalized inverse of E.
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What are Schur complements, anyway?
Linear Algebra and its Applications, 1986 This paper treats the Schur complement of a partitioned matrix whose use goes back more than 130 years. It shows how several modern manifestations of this concept can be viewed in a unified way. Classically, Schur complements can be used to determine the rank of partitioned matrices.
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A new method for solving the elliptic curve discrete logarithm problem [PDF]
Groups, Complexity, Cryptology, 2021 The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem.
Ansari Abdullah +2 more
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Idempotent operator and its applications in Schur complements on Hilbert C*-module
Special Matrices, 2023 The present study proves that TT is an idempotent operator if and only if R(I−T∗)⊕R(T)=X{\mathcal{ {\mathcal R} }}\left(I-{T}^{\ast })\oplus {\mathcal{ {\mathcal R} }}\left(T)={\mathcal{X}} and (T∗T)†=(T†)2T{\left({T}^{\ast }T)}^{\dagger }={\left({T ...
Karizaki Mehdi Mohammadzadeh +1 more
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Schur Complement-Based Infinity Norm Bounds for the Inverse of GDSDD Matrices
Mathematics, 2022 Based on the Schur complement, some upper bounds for the infinity norm of the inverse of generalized doubly strictly diagonally dominant matrices are obtained. In addition, it is shown that the new bound improves the previous bounds.
Yating Li, Yaqiang Wang
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Some counterexamples related to sectorial matrices and matrix phases
Examples and Counterexamples, 2021 A sectorial matrix is an n×nmatrix whose numerical range is contained in an open half-plane, and such matrices have many nice properties. In particular, the subset of strictly accretive matrices is a convex cone in the space of n×nmatrices, and results ...
Xin Mao, Li Qiu, Axel Ringh, Dan Wang
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International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as self‐interest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
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Duality in elliptic Ruijsenaars system and elliptic symmetric functions
European Physical Journal C: Particles and Fields, 2021 We demonstrate that the symmetric elliptic polynomials $$E_\lambda (x)$$ E λ ( x ) originally discovered in the study of generalized Noumi–Shiraishi functions are eigenfunctions of the elliptic Ruijsenaars–Schneider (eRS) Hamiltonians that act on the ...
A. Mironov, A. Morozov, Y. Zenkevich
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