scholarly journals The boundary of the Krein space tracial numerical range, an algebraic approach and a numerical algorithm

2009 ◽  
Vol 189 (4) ◽  
pp. 539-551
Author(s):  
N. Bebiano ◽  
H. Nakazato ◽  
A. Nata ◽  
J. da Providência
Keyword(s):  
Numerical Algorithm ◽  
Numerical Range ◽  
Krein Space ◽  
Algebraic Approach ◽  
Kreĭn Space

scholarly journals More on geometry of Krein space C-numerical range

2019 ◽  
Vol 352 ◽  
pp. 258-269
Author(s):  
Alexander Guterman ◽  
Rute Lemos ◽  
Graça Soares
Keyword(s):  
Numerical Range ◽  
Krein Space ◽  
Kreĭn Space

scholarly journals Computing the numerical range of Krein space operators

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Natalia Bebiano ◽  
J. da Providência ◽  
A. Nata ◽  
J.P. da Providência
Keyword(s):  
Hilbert Space ◽  
Quadratic Form ◽  
Numerical Range ◽  
Krein Space ◽  
Inner Product ◽  
Indefinite Inner Product ◽  
Finite Dimensional ◽  
Alternative Algorithm ◽  
Kreĭn Space ◽  
Finite Dimensional Case

Abstract Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined elliptical and hyperbolical numerical ranges. The numerical results reported here indicate that this method is very efficient, since it is faster and more accurate than either of the existing algorithms. Further, it may yield easy solutions for the inverse indefinite numerical range problem. Our algorithm uses an idea of Marcus and Pesce from 1987 for generating Hilbert space numerical ranges of matrices of size n.

The numerical range of linear operators on the 2-dimensional Krein space

2011 ◽  
Vol 22 ◽  
Author(s):  
Hiroshi Nakazato ◽  
Natalia Bebiano ◽  
Joao Da Providencia
Keyword(s):  
Numerical Range ◽  
Krein Space ◽  
Linear Operators ◽  
Kreĭn Space

The Numerical Range of 2-Dimensional Krein Space Operators

2008 ◽  
Vol 51 (1) ◽  
pp. 86-99 ◽  
Author(s):  
Hiroshi Nakazato ◽  
Natália Bebiano ◽  
João da Providência
Keyword(s):  
Hilbert Spaces ◽  
Numerical Range ◽  
Krein Space ◽  
Kreĭn Space

AbstractThe tracial numerical range of operators on a 2-dimensional Krein space is investigated. Results in the vein of those obtained in the context of Hilbert spaces are obtained.

Krein Space-based Hθ Fault Estimation for Linear Discrete Time-varying Systems

2009 ◽  
Vol 34 (12) ◽  
pp. 1529-1533 ◽  
Author(s):  
Mai-Ying ZHONG ◽  
Shuai LIU ◽  
Hui-Hong ZHAO
Keyword(s):  
Discrete Time ◽  
Krein Space ◽  
Fault Estimation ◽  
Time Varying ◽  
Time Varying Systems ◽  
Kreĭn Space

scholarly journals A Krein space-based approach to event-triggered H∞ filtering for linear discrete time-varying systems

Automatica ◽  
2022 ◽  
Vol 135 ◽  
pp. 110001
Author(s):  
Maiying Zhong ◽  
Steven X. Ding ◽  
Qing-Long Han ◽  
Xiao He ◽  
Donghua Zhou
Keyword(s):  
Discrete Time ◽  
Krein Space ◽  
Time Varying ◽  
Time Varying Systems ◽  
Kreĭn Space ◽  
Event Triggered
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