Eigenvalue Estimates Using the Kolmogorov-Sinai Entropy

نویسنده

  • Shih-Feng Shieh
چکیده

The scope of this paper is twofold. First, we use the Kolmogorov-Sinai Entropy to estimate lower bounds for dominant eigenvalues of nonnegative matrices. The lower bound is better than the Rayleigh quotient. Second, we use this estimate to give a nontrivial lower bound for the gaps of dominant eigenvalues ofA and A+V.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Observational Modeling of the Kolmogorov-Sinai Entropy

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...

متن کامل

Entropy of infinite systems and transformations

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...

متن کامل

The Problem of Positive Kolmogorov-Sinai entropy for the Standard map

The problem of positive Kolmogorov-Sinai entropy of the Chirikov-Standard map Tλf : (x, y) 7→ (2x − y + λf(x), x) with f(x) = sin(x) with respect to the invariant Lebesgue measure on the two-dimensional is open. In 1999, we believed to have a proof that the entropy can be bounded below by log(λ/2)−C(λ) with C(λ) = arcsinh(1/λ) + log(2/ √ 3) and that for λ > λ0 = (8/(6− 3 √ 3)) = 3.1547..., the ...

متن کامل

A Revised Generalized Kolmogorov-Sinai-like Entropy and Markov Shifts

The Kolmogorov-Sinai entropy in the sense of Tsallis under Bernoulli shifts was obtained by Mesón and Vericat [J. Math. Phys. 37, 4480(1996)]. In this paper, we propose a revised generalized Kolmogorov-Sinai-q entropy under Markov shifts. The form of this generalized entropy with factor q is nonextensive. The new generalized entropy contains the classical Kolmogorov-Sinai entropy and Renýı entr...

متن کامل

On the Connections of Generalized Entropies With Shannon and Kolmogorov-Sinai Entropies

We consider the concept of generalized Kolmogorov–Sinai entropy, where instead of the Shannon entropy function, we consider an arbitrary concave function defined on the unit interval, vanishing in the origin. Under mild assumptions on this function, we show that this isomorphism invariant is linearly dependent on the Kolmogorov–Sinai entropy.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Entropy

دوره 13  شماره 

صفحات  -

تاریخ انتشار 2011