Upper Bounds on the Distribution of the Condition Number of Singular Matrices Bornes Supérieures pour la fonction de distribution du conditionnement des Matrices Singulières
نویسندگان
چکیده
We exhibit upper bounds for the probability distribution of the generalized condition number of singular complex matrices. To this end, we develop a new technique to study volumes of tubes about projective varieties in the complex projective space. As a main outcome, we show an upper bound estimate for the volume of the intersection of a tube with an equi–dimensional projective algebraic variety.
منابع مشابه
General formulas for the smoothed analysis of condition numbers
We provide estimates on the volume of tubular neighborhoods around a subvariety Σ of real projective space, intersected with a disk of radius σ . The bounds are in terms of σ , the dimension of the ambient space, and the degree of equations defining Σ . We use these bounds to obtain smoothed analysis estimates for some conic condition numbers. To cite this article: P. Bürgisser et al., C. R. Ac...
متن کاملSpecial Cases of the Parking Functions Conjecture and Upper-Triangular Matrices
We examine the q = 1 and t = 0 special cases of the parking functions conjecture. The parking functions conjecture states that the Hilbert series for the space of diagonal harmonics is equal to the bivariate generating function of area and dinv over the set of parking functions. Haglund recently proved that the Hilbert series for the space of diagonal harmonics is equal to a bivariate generatin...
متن کاملPrecise Estimates for the Subelliptic Heat Kernel on H-type Groups
We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups G of H-type. Specifically, we show that there exist positive constants C1, C2 and a polynomial correction function Qt on G such that C1Qte − d2 4t ≤ pt ≤ C2Qte d2 4t where pt is the heat kernel, and d the Carnot-Carathéodory distance on G. We also obtain similar bounds on the norm of its subellip...
متن کاملUpper and Lower Bounds on Overflow Probabilities for a Multiplexer with Multiclass Markovian Sources
In this paper, we consider a multiplexer with constant output rate and innnite buuer capacity fed by independent Markovian uid on-oo sources. We do not assume that the model is symmetrical: there is an arbitrary number K of diierent traac classes, and for each class k, an arbitrary number N k of sources of class k. We derive lower and upper bounds for the stationary distribution of the backlog ...
متن کاملمعمای معاهده حق مؤلف سازمان جهانی مالکیت فکری مصوب 1996
Le traite de l’OMPI sur le droit d’auteur de 1996 est venu completer et mettre à jour la convention de Berne. Il a, dans une large mesure, reussie d’atteindre ses objectifs surtout pour; l’adoption des compilations de donnees sous quelque forme que ce soit, et de logiciel comme creations intellectuelles; la precision du droit de location pour les auteurs de progra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005