Results 251 to 260 of about 2,985,813 (306)
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On the Inertia of Intervals of Matrices
SIAM Journal on Matrix Analysis and Applications, 1990The inertia of intervals and lines of matrices is investigated. For complex $n \times n$ matrices A and B it is shown that, under mild nonsingularity conditions, $A + tB$ changes inertia at no more than $n^2 $ real values of t. Conditions are given for the constancy of the inertia of $A + tB$, where t lies in a real interval.
Daniel Hershkowitz, Hans Schneider
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On the eigenvalues of interval matrices
26th IEEE Conference on Decision and Control, 1987In this paper we will examine how the spectrum (of eigenvalues) of an interval matrix family M depends on the spectrum of its extreme sets. We present three results: 1) We show that the roots of pairwise convex combinations of the characteristic polynomials of the vertices of M provide a bound for the spectrum of M.
C. Hollot, A. Bartlett
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On nilpotent interval matrices
2019In this paper, we give a necessary and sufficient condition for the powers of an interval matrix to be nilpotent. We show an interval matrix $it{bf{A}}$ is nilpotent if and only if $ rho(mathscr{B})=0 $, where $mathop{mathscr{B}} $ is a point matrix, introduced by Mayer (Linear Algebra Appl. 58 (1984) 201-216), constructed by the $ (*) $ property.
Raboky, Effat Golpar, Eftekhari, Tahereh
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Interval Matrices: Singularity and Real Eigenvalues
SIAM Journal on Matrix Analysis and Applications, 1993An interval matrix \(A_ I=(A_ c-\Delta,A_ c+\Delta)\) is called singular if it contains a singular matrix. Here, \(A_ c\) and \(\Delta\) are real \(n\times n\) matrices and \(\Delta\) nonnegative. It is shown that a singular interval matrix \(A_ I\) contains a singular matrix of a special type, i.e., \(A_ s=A_ c-dT_ y\Delta T_ x\) where \(0\leq d\leq 1\
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Regularity of Interval Matrices and Theorems of the Alternatives
Reliable Computing, 2006Given an interval matrix \({\mathbf A}\) the author presents necessary and sufficient conditions for all \(A\in{\mathbf A}\) to be regular. Some of these criteria are used to prove results on the alternatives for inequalities involving absolute values.
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Positive Definiteness and Stability of Interval Matrices
SIAM Journal on Matrix Analysis and Applications, 1994Interval matrices are considered that are positive definite, positive semidefinite, Hurwitz stable or Schur stable. Necessary and sufficient conditions for each of these properties are investigated. The conditions are based on corresponding properties of a finite number of real test matrices that are derived from the interval matrix under consideration.
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On sufficient conditions for the stability of Interval matrices
Journal of the Franklin Institute, 1989New sufficient conditions are developed for the stability analysis of an interval matrix [B,C]. The approach presented uses similarity transformations diagonalizing a matrix \(A\in [B,C]\) and an estimate of the norm of the error matrix. Numerical examples are given.
Chou, Jyh-Horng, Horng, Ing-Rong
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Stability of interval matrices
International Journal of Control, 1987In this paper new sufficient conditions for stability and complete instability of an interval matrix JV(P, Q) are presented. They include the corresponding results derived by Heinen (1984) and Xu Daoyi (1985) as particular cases. Secondly, we present the concept of composite type for stability, and simple criteria for this type.
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Simultaneous Schur stability of interval matrices
Automatica, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mau-Hsiang Shih, Chin-Tzong Pang
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Computational and Applied Mathematics, 2022
Tuğçe Aydın, Serdar Enginoğlu
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Tuğçe Aydın, Serdar Enginoğlu
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