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The steady-state of the (Normalized) LMS is schur convex
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016In this work, we demonstrate how the theory of majorization and schur-convexity can be used to assess the impact of input-spread on the Mean Squares Error (MSE) performance of adaptive filters. First, we show that the concept of majorization can be utilized to measure the spread in input-regressors and subsequently order the input-regressors according ...
Khaled A. Al-Hujaili +2 more
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Directional-Quasi-Convexity, Asymmetric Schur-Convexity and Optimality of Consecutive Partitions
Mathematics of Operations Research, 1996The current paper has the following distinct goals: 1. To generalize standard quasi-convexity to obtain a weaker property of functions that suffices for optimality of extreme points. Specifically, it is required that intersections of the level sets of the function with line segments having direction in a prescribed set are convex. 2. To characterize
Frank K. Hwang, Uriel G. Rothblum
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Schur-convex robustness measures in dynamical networks
2014 American Control Conference, 2014We investigate robustness of networks with linear time-invariant dynamics under external stochastic disturbances. We propose a partial ordering on this class of dynamical networks and exploit their structural properties to characterize their robustness properties and fundamental limits.
Milad Siami, Nader Motee
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Schur Stability of Convex Combinations of Complex Polynomials
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2007This letter concerns the Schur stability of convex combinations of complex polynomials. For given two Schur stable complex polynomials, a sufficient condition is given such that the convex combination of polynomials is also Schur stable.
Younseok Choo, GinKyu Choi
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SCHUR CONVEX FUNCTIONALS: FATOU PROPERTY AND REPRESENTATION
Mathematical Finance, 2010The Fatou property for every Schur convex lower semicontinuous (l.s.c.) functional on a general probability space is established. As a result, the existing quantile representations for Schur convex l.s.c. positively homogeneous convex functionals, established on for either p= 1 or p=∞ and with the requirement of the Fatou property, are generalized for
Grechuk, Bogdan, Zabarankin, Michael
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Convex combinations of matrices — Nonsingularity and Schur stability
1997Using the notion of a block P-matrix, introduced previously by the authors, a characterization of the nonsingularity (Schur stability, resp.) of all convex combinations of three nonsingular (Schur stable, resp.) real matrices is derived.
Ludwig Elsner, Tomasz Szulc
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2010
The property of Schur-covexity (Schur-concavity) of means is considered and compared with recent results in the literature [1], [4], [2], [3]. A new proof for convexity (concavity) and Schur- covexity (Schur-concavity) of the integral arithmetic mean is done. We established the sufficient conditions such that the generalized quasi-arithmetic mean Mf (k
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The property of Schur-covexity (Schur-concavity) of means is considered and compared with recent results in the literature [1], [4], [2], [3]. A new proof for convexity (concavity) and Schur- covexity (Schur-concavity) of the integral arithmetic mean is done. We established the sufficient conditions such that the generalized quasi-arithmetic mean Mf (k
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Characterization of Inner Product Spaces by Strongly Schur-Convex Functions
Results in Mathematics, 2020Mirosław Adamek
exaly
Schur-Convex Functions on ℓp\ell ^p Spaces and Applications
Results in Mathematics, 2022Ali Bayati Eshkaftaki
exaly