The diagonal equivalence of a nonnegative matrix to a stochastic matrix

Brualdi, Richard A.; Parter, Seymour V.; Schneider, Hans

doi:10.1016/0022-247x(66)90184-3

Cited by 145 publications

(60 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Below we use an alternative perspective, which relates PEFF solutions to positive eigenvectors of a nonlinear mapping. The analogous approach in the context of IPFP has been pioneered by Menon (1967) and Brualdi et al (1966).…”

Section: Introductionmentioning

confidence: 99%

The composite iteration algorithm for finding efficient and financially fair risk-sharing rules

Pazdera

Schumacher

Werker

2017

Journal of Mathematical Economics

View full text Add to dashboard Cite

The composite iteration algorithm for finding efficient and financially fair risk-sharing rules Pazdera, J.; Schumacher, J.M.; Werker, B.J.M. Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. AbstractWe consider the problem of finding an efficient and fair ex-ante rule for division of an uncertain monetary outcome among a finite number of von Neumann-Morgenstern agents. Efficiency is understood here, as usual, in the sense of Pareto efficiency subject to the feasibility constraint. Fairness is defined as financial fairness with respect to a predetermined pricing functional. We show that efficient and financially fair allocation rules are in one-to-one correspondence with positive eigenvectors of a nonlinear homogeneous and monotone mapping associated to the risk sharing problem. We establish relevant properties of this mapping. On the basis of this, we obtain a proof of existence and uniqueness of solutions via nonlinear Perron-Frobenius theory, as well as a proof of global convergence of the natural iterative algorithm. We argue that this algorithm is computationally attractive, and discuss its rate of convergence.

show abstract

Section: Introductionmentioning

confidence: 99%

The composite iteration algorithm for finding efficient and financially fair risk-sharing rules

Pazdera

Schumacher

Werker

2017

Journal of Mathematical Economics

View full text Add to dashboard Cite

show abstract

“…When per(A) > 0, that the intersection is nonempty was established by Brualdi, Parter and Schneider [7]. Uniqueness, when nonempty, follows from the fact that distinct doubly-stochastic matrices cannot have identical profiles, given as Corollary 2.6.6 in Bapat and Raghavan [6].…”

Section: Theorem 1 For Any N × N Biadjacency Matrix a Resulting Frommentioning

confidence: 97%

An Accurate System-Wide Anonymity Metric for Probabilistic Attacks

Bagai

et al. 2011

Privacy Enhancing Technologies

View full text Add to dashboard Cite

Abstract.We give a critical analysis of the system-wide anonymity metric of Edman et al. [3], which is based on the permanent value of a doubly-stochastic matrix. By providing an intuitive understanding of the permanent of such a matrix, we show that a metric that looks no further than this composite value is at best a rough indicator of anonymity. We identify situations where its inaccuracy is acute, and reveal a better anonymity indicator. Also, by constructing an information-preserving embedding of a smaller class of attacks into the wider class for which this metric was proposed, we show that this metric fails to possess desirable generalization properties. Finally, we present a new anonymity metric that does not exhibit these shortcomings. Our new metric is accurate as well as general.

show abstract

“…In closing this Subsection, it is worthwhile recalling that, for a large class of irreducible stochastic matrices m, it is possible to find positive diagonal matrices D 1 and D 2 such that D 1 · m · D 2 is a doubly stochastic matrix, see Brualdi et al (1966) and Sinkhorn and Knopp (1967).…”

Section: Double Stochastic Matrices and Unstable Periodic Orbitsmentioning

confidence: 99%

Cyclic Markov chains with an application to an intermediate ENSO model

Pasmanter

Timmermann²

2003

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

Abstract.We develop the theory of cyclic Markov chains and apply it to the El Niño-Southern Oscillation (ENSO) predictability problem. At the core of Markov chain modelling is a partition of the state space such that the transition rates between different state space cells can be computed and used most efficiently. We apply a partition technique, which divides the state space into multidimensional cells containing an equal number of data points. This partition leads to mathematical properties of the transition matrices which can be exploited further such as to establish connections with the dynamical theory of unstable periodic orbits. We introduce the concept of most and least predictable states. The data basis of our analysis consists of a multicentury-long data set obtained from an intermediate coupled atmosphere-ocean model of the tropical Pacific. This cyclostationary Markov chain approach captures the spring barrier in ENSO predictability and gives insight also into the dependence of ENSO predictability on the climatic state.

show abstract

The diagonal equivalence of a nonnegative matrix to a stochastic matrix

Cited by 145 publications

References 5 publications

The composite iteration algorithm for finding efficient and financially fair risk-sharing rules

The composite iteration algorithm for finding efficient and financially fair risk-sharing rules

An Accurate System-Wide Anonymity Metric for Probabilistic Attacks

Cyclic Markov chains with an application to an intermediate ENSO model

Contact Info

Product

Resources

About