Results 81 to 90 of about 50,277 (117)
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The NLMS Is Steady-State Schur-Convex
IEEE Signal Processing Letters, 2021In this work, we study the impact of input-spread on the steady-state excess mean squared error (EMSE) of the normalized least mean squares (NLMS) algorithm. First, we use the concept of majorization to order the input-regressors according to their spread.
Anum Ali +2 more
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Strong Schur-Convexity of the Integral Mean
Results in Mathematics, 2023The strong Schur-convexity of the integral mean as well as of the left and right gaps in the Hermite- Hadamard inequality for strongly convex functions are proved. An useful characterization of strongly Schur convex functions F : I-n -> R by partial derivatives is given.
Mirosław Adamek +2 more
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Schur-convexity and Schur-geometrically concavity of Gini means [PDF]
Computers and Mathematics With Applications, 2009 The Schur-convexity and the Schur-geometric convexity with variables (x,y)∈R++2 for fixed (s,t) of Gini means G(r,s;x,y) are discussed.
Huan-Nan Shi
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Schur Convexity for a Class of Symmetric Functions
2011The Schur-convex function was introduced by I. Schur in 1923, and it has many important applications in analytic inequalities, generalized means, statistics experiment, chart and matrix, combinatorial optimization, reliability, information security, random sorting, etc.
Shuhong Wang, Tian-Yu Zhang, Bo-Yan Xi
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2010
For any given partial ordering \(\preceq\)of a setX, real-valued functionsf1 defined onXwhich satisfyf(x)= f(y) wheneverx_yare var- 2 iously referred to as “monotonic,” “isotonic,” or “order-preserving.” 3 For the ordering of majorization, the order-preserving functions were 4 first systematically studied by I. Schur (1923).
Albert W. Marshall +2 more
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For any given partial ordering \(\preceq\)of a setX, real-valued functionsf1 defined onXwhich satisfyf(x)= f(y) wheneverx_yare var- 2 iously referred to as “monotonic,” “isotonic,” or “order-preserving.” 3 For the ordering of majorization, the order-preserving functions were 4 first systematically studied by I. Schur (1923).
Albert W. Marshall +2 more
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Schur-convexity and quadrature formulae
Mathematische Nachrichten, 2015This paper aims to contribute to the exploration of quadrature formulae by proving that the error of a quadrature formula has the Schur-convexity property. The emphasis is on the quadrature formulae with the maximum degree of precision. The Schur-convexity of the error has an interesting implication – the monotonicity of the error. Namely, it turns out
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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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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 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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Partition-Optimization with Schur Convex Sum Objective Functions
SIAM Journal on Discrete Mathematics, 2004Summary: We study optimization problems over partitions of the finite set \(N = {1,\dots, n}\), where each element \(i\) in the partitioned set \(N\) is associated with a real number \(\theta^i\) and the objective associated with a partition \(\pi=(\pi_, \ldots, \pi_p)\) has the form \(F(\pi)=f(\theta_{\pi})\), where \( \theta_{\pi} = (\sum_{i\in{\pi_1}
Frank Kwang-Ming Hwang +1 more
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