Factbites
 Where results make sense
About us   |   Why use us?   |   Reviews   |   PR   |   Contact us  

Topic: Majorization


Related Topics

  
  PlanetMath: majorization
Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, 1979, Acadamic Press, New York.
This is version 5 of majorization, born on 2004-07-28, modified 2006-11-11.
Object id is 6043, canonical name is Majorization.
planetmath.org /encyclopedia/Majorize.html   (71 words)

  
  Weekly Calendar   (Site not responding. Last check: )
The distribution (yi) is majorized by the distribution (xi) if for any k, the total wealth of the k most poor people in (yi) is no less than the total wealth of the k most poor people in (xi).
Characterizations of majorization are available in terms of geometry, probability, convex functions and linear algebra; the proofs for equivalences involve several fundamental results in functional analysis.
Majorization should be defined in terms of stochastic processes while 'poverty' demands a simple and practical definition.
www-math.bgsu.edu /oldcalendars/1998-10-19.html   (235 words)

  
 Matrix Majorization (ResearchIndex)
Abstract: We study the concept matrix majorization: for two real matrices A and B having m rows we say that A majorizes B if there is a row-stochastic matrix X with AX = B. A special case is classical notion of vector majorization.
Several properties and characterizations of matrix majorization are given.
2 The doubly stochastic matrices of a vector majorization (context) - Brualdi - 1984
citeseer.ist.psu.edu /54167.html   (306 words)

  
 Rustam Ibragimov
The majorization relation is a formalization of the concept of diversity in the components of vectors.
Over the past decades, majorization theory, which focuses on the study of this relation and functions that preserve it, has found applications in disciplines ranging from statistics, probability theory and economics to mathematical genetics, linear algebra and geometry.
This is the first probabilistic result that shows that majorization properties of log-concave densities are reversed for a wide class of distributions and is the key to reversals of properties of many economic models built upon the popular log-concavity assumption.
www.econ.yale.edu /graduate/placement/2004-05/ibragimov.htm   (2063 words)

  
 Electronic Resources
The dissertation provides a unified approach to the study of a number of important problems in economic theory, mathematical finance and econometrics using new majorization theory and martingale convergence methods.
The first chapter develops a unified approach to the analysis of several models in economics that depend on the majorization properties of convolutions of distributions.
The second chapter of the dissertation presents applications of the new majorization theory developed in Chapter 1 to the study of properties of inheritance models that have been a subject of an increasing interest in economics in recent years and analyzes robustness of these models to heavy-tailedness of traits.
sunzi1.lib.hku.hk /ER/detail/3520109   (154 words)

  
 EECS News and Events
The performance of demand-driven caching is known to depend on the locality of reference exhibited by the stream of requests made to the cache.
As we propose to measure strength of locality of reference in a stream of requests through the skewness of its popularity distribution, we introduce the notion of majorization as a means of capturing this degree of skewness.
In addition, we explore how the majorization of popularity distributions translates into comparisons of three well-known locality of reference metrics, namely the inter-reference time, the working set size and the stack distance.
www.eecs.umich.edu /eecs/etc/events/abst.cgi?264   (296 words)

  
 Majorization in Economic Disparity Measure   (Site not responding. Last check: )
This survey presents an account of univariate and multivariate majorization orderings and their characterization by various classes of economic disparity indices.
First, a concise treatment of classical univariate results is given, including majorization with different means and different population sizes, as well as Lorenz orderings of relative and absolute disparity.
Third, disparity in several attributes and multivariate majorization are investigated, and a multivariate version of the Lorenz curve is introduced.
www.uni-koeln.de /wiso-fak/wisostatsem/abstracts/maecdime/maecdime.html   (99 words)

  
 CU-Denver Department of Mathematics Events
This talk presents several new perturbation theorems involving a general inequality and majorization of principal angles for subspaces of a finite dimensional space that holds for arbitrary unitarily invariant norms.
One new theorem involves perturbations where the absolute value of the difference of the squares of the cosines/sines are majorized by the sines of the angles between the perturbed subspaces.
The other theorems involve upper bounds for proximity of the Ritz values in terms of the proximity of the trial subspaces without making an assumption that the trial subspace is close to an invariant subspace.
www-math.cudenver.edu /events/QueryEvent.php?eid=211   (279 words)

  
 POP --- Partial Order Programming
Majorization with respect to a partial order is shown to be a special case of majorization as exchangeability.
In this special case, the resulting majorization order always defines a distributive lattice that is isomorphic to the standard real vector lattice.
In classical majorization theory, the semigroup of doubly-stochastic matrices plays a crucial role, both in the definition of majorization and in the modeling of exchange.
www.cs.ucla.edu /~stott/pop   (784 words)

  
 University Of Tampere - Dissertation information
Majorization and k-majorization as an approach to some problems in optimization and eigenvalue estimation
In the first part, we survey relevant results on majorization and Schur-convexity and produce some auxiliary results needed later.
In the third part, we generalize the majorization order to what we call k-majorization.
acta.uta.fi /english/teos.phtml?10903   (296 words)

  
 Design orderings based on the information matrix   (Site not responding. Last check: )
Moreover, if two lists of eigenvalues are ordered by majorization, then the corresponding lists of canonical variances are ordered by weak majorization.
Consequently, weak majorization can sometimes be determined for canonical variances over the reference universe via the corresponding eigenvalues of information matrices.
Each of these three criteria is a summary measure of scatter of variances, not of magnitude; minimizing over too large a class will reduce scatter at the cost of increasing magnitude.
www.designtheory.org /library/extrep/html/node30.html   (923 words)

  
 Quantum Information: Problem 4
Thus A can be converted to B if and only if the eigenvalue sequence of the restriction of A is more mixed than that of B in the sense of majorization of probability vectors [Maj].
The above problem can be rephrased completely in this context of majorization of classical probability vectors, since tensoring pure bipartite states means again tensoring of probability vectors for the eigenvalues of the reduced density operators.
A. Marshal and I. Olkin, »Inequalities: Theory of Majorization and Its Applications«, Academic Press (1979) and, in the quantum context,
www.csci.csusb.edu /ykarant/courses/sp2004/csci121/beam-up-ghoulash/quantum-information1/qi/problems/4.html   (479 words)

  
 Quantum Information: Problem 4
Thus A can be converted to B if and only if the eigenvalue sequence of the restriction of A is more mixed than that of B in the sense of majorization of probability vectors [Maj].
There is some further literature on the use of majorization for the characterization of pure state entanglement [V1], [JP2], [VJN1], [N2] and on catalysis [EW1] that may be useful.
We have avoided the use of a comparison symbol, or the terminology "p is majorized by q'', because there are different conventions in the literature.
www.imaph.tu-bs.de /qi/problems/4.html   (496 words)

  
 Design orderings based on the information matrix
Moreover, if two lists of eigenvalues are ordered by majorization, then the corresponding lists of canonical variances are ordered by weak majorization.
Consequently, weak majorization can sometimes be determined for canonical variances over the reference universe via the corresponding eigenvalues of information matrices.
Each of these three criteria is a summary measure of scatter of variances, not of magnitude; minimizing over too large a class will reduce scatter at the cost of increasing magnitude.
designtheory.org /library/extrep/html/node30.html   (923 words)

  
 CJO - Abstract - EFFICIENCY OF LINEAR ESTIMATORS UNDER HEAVY-TAILEDNESS: CONVOLUTIONS OF [alpha]-SYMMETRIC DISTRIBUTIONS   (Site not responding. Last check: )
This paper focuses on the analysis of efficiency, peakedness, and majorization properties of linear estimators under heavy-tailedness assumptions.
We demonstrate that peakedness and majorization properties of log-concavely distributed random samples continue to hold for convolutions of [alpha]-symmetric distributions with [alpha] > 1.
The results in this paper constitute a part of the author's dissertation “New Majorization Theory in Economics and Martingale Convergence Results in Econometrics” presented to the faculty of the Graduate School of Yale University in candidacy for the degree of Doctor of Philosophy in Economics in March 2005.
journals.cambridge.org /action/displayAbstract?fromPage=online&aid=989256   (252 words)

  
 The Maseeh Mathematics & Statistics Colloquium Series   (Site not responding. Last check: )
Abstract: Classical majorization admits a colorful interpretation as an ordering of wealth inequality that is essentially determined by the acceptance of the axiom that robbing a little from the rich and giving it to the poor will decrease inequality.
However majorization and its first cousin, the Lorenz order, have a role to play in an enormously diverse array of settings.
Any problem whose solution is a vector of the form (c,c,…,c) may well be susceptible to rephrasing in terms of some cleverly chosen Schur convex function and its extreme value under the majorization ordering.
www.mth.pdx.edu /Events/colloquium.asp?id=55   (169 words)

  
 Approximate Majorization - Dicy.com
Citations Using approximate majorization to characterize protocol fairness...
Adam Meyerson Using approximate majorization to characterize protocol...
We propose the use of approximate majorization as a framework for...
www.dicy.com /search.cfm?st=approximate%20majorization   (87 words)

  
 Front: [arXiv:0710.5566] Majorization for infinite sequences, an extension of the Schur-Horn Theorem, and operator ...
Front: [arXiv:0710.5566] Majorization for infinite sequences, an extension of the Schur-Horn Theorem, and operator ideals
Further results on majorization for infinite sequences providing "intermediate" sequences generalize known results from the finite case.
Majorization properties and invariance under various classes of stochastic matrices are then used to characterize arithmetic mean closed operator ideals.
front.math.ucdavis.edu /0710.5566   (128 words)

  
 EconPapers: Rank Reduction of Correlation Matrices by Majorization
The algorithm is based on majorization and, therefore, it is globally convergent.
A simulation study suggests that majorization compares favourably with competing approaches in terms of the quality of the solution within a fixed computational time.
The problem of rank reduction of correlation matrices occurs when pricing a derivative dependent on a large number of assets, where the asset prices are modelled as correlated log-normal processes.
econpapers.repec.org /paper/wpawuwpfi/0502006.htm   (222 words)

  
 v10n2
In the paper, new upper bounds in the second Kershaw's double inequality and its generalizations involving the gamma, psi and polygamma functions are established, some known results are refined.
We enlarge two weak majorization relations of the vectors to strong majorization relations of the vectors.
An improvement of the discrete Steffensen's inequalities is established by the related propositions in the theory of majorization.
rgmia.vu.edu.au /v10n2.html   (833 words)

  
 Foundations and Trends in Communications and Information Theory - Business News and Articles
This short tutorial presents two mathematical techniques namely Majorization Theory and Matrix-Monotone Functions which are applied to solve communication and information theoretic problems in.
Daniel P. Palomar would like to thank his Ph.D. advisor, Miguel Angel Lagunas, and his mentor at Stanford University, John Cioffi, for their inspiring support at a time when he was starting an.
This text has developed a unified framework, based on majorization theory, for the optimal design of linear and nonlinear decision-feedback MIMO transceivers in point-to-point MIMO communication.
www.entrepreneur.com /tradejournals/pub/5DFD.html   (751 words)

  
 Amazon.com: Majorization
Inequalities: Theory of Majorization and Its Applications (Springer Series in Statistics) by Albert W. Marshall, Ingram Olkin, and Barry Arnold (Hardcover - Jan 1, 2009)
Majorization and Matrix Monotone Functions in Wireless Communications (Foundations and Trends in Communcations and Information Theory) by Eduard Jorswieck and Holger Boche (Paperback - Jul 11, 2007)
Majorization and the Lorenz Order: Brief Introduction (Lecture Notes in Statistics) by Barry C. Arnold (Paperback - Dec 1987)
www.amazon.com /s?ie=UTF8&keywords=Majorization&index=blended&page=1   (598 words)

  
 Abstract   (Site not responding. Last check: )
The best previously known results for the multiple-choice processes in the heavily loaded case were obtained by majorization from the single-choice process.
We show, however, that the multiple-choice processes are fundamentally different from the single-choice variant in that they have "short memory".
We present a majorization result showing that the always-go-left scheme obtains a better load balancing than the greedy scheme for any choice of n, m, and d.
www.cis.njit.edu /~czumaj/PUBLICATIONS/STOC00-Bins-and-Balls.html   (399 words)

  
 Journal of Convex Analysis, Vol. 5, No. 1, pp. 81-105, 1998   (Site not responding. Last check: )
Abstract: In this paper the problem of the isotonicity of a function with respect to a group majorization is discussed.
As an application, a characterization of the isotonicity of a quadratic form and a linear form is presented.
In addition, it is shown that the conditions are necessary and sufficient for a group majorization to be a group induced cone ordering.
www.emis.de /journals/JCA/vol.5_no.1/7.html   (188 words)

  
 [No title]
As classical examples of majorization theorems, one could mention the theorem of Dodds and Fremlin on compact operators and the theorem of Lozanovskii, Buhvalov and Schep on band properties of the space of integral operators.
By using the permanence theorem of the theory of principal modules it was possible to elaborate a unified method for the study of majorization problems which allowed to redemonstrate, on a common basis, most of the known majorization theorems (in particular the ones mentioned above) and to find new results.
Among the new results found with the aid of that method, one mentions the results in [19] and [28] on approximable operators and the results in [19], [21] and [28] on the relation between the order ideal and the closed algebraic ideal generated by a regular operator.
www.imar.ro /~dvuza/HOMEPAGE/OVERVIEW.HTM   (686 words)

  
 EQUIP --- publication details   (Site not responding. Last check: )
We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms considered in the canonical decomposition.
This property is a consequence of the structure of the initial state and of the QFT, based on controlled-phase operators and a single action of a Hadamard gate per qubit.
We also prove that majorization in phase-estimation algorithms follows in a most natural way from unitary evolution, unlike its counterpart in Grover's algorithm.
www.equip.qipc.org /bin/pubfull?f_node=&f_label=OLM1-02&f_ticket=   (145 words)

  
 RR-2116 : Burst reduction properties of rate-control throttles : departure process   (Site not responding. Last check: )
Using sample path methods and the notion of majorization, we analyze the effect that parameters such as the token buffezr capacity and token genration period have on the vector of interdeparture times.
In the transient case, we establish the monotonicity of the burst reduction in the sense of the majorization.
Utilisant des techniques d'analyse trajectorielle et la notion de majoration, nous analysons les effets de modification des parametres, tel que la taille du tampon de jetons et la frequence de generation des jetons, sur le vecteur des durees d'interdepart- s.
www.inria.fr /rrrt/rr-2116.html   (303 words)

  
 MathLinks Math Forums :: View topic - The Karamata inequality
The definition of majorizing and minorizing number arrays I gave above was mathematically clear but quite long and not plastic.
Karamata published later than Hardy,Littlewood and Polya, and in any case majorization was independently discovered many times before and after all these publications.
In the Anglo-Saxon countries it is called "majorization inequality" or "Hardy-Littlewood-Polya" majorization inequality".
www.mathlinks.ro /Forum/viewtopic.php?t=14975   (1192 words)

Try your search on: Qwika (all wikis)

Factbites
  About us   |   Why use us?   |   Reviews   |   Press   |   Contact us  
Copyright © 2005-2007 www.factbites.com Usage implies agreement with terms.