Preprint 0 ( 1999 ) ? { ? 1 Asymptotic Convergence of Degree
نویسنده
چکیده
It is well known that the degree-raised Bernstein-B ezier coeecients of degree n of a polynomial g converge to g at the rate 1=n. In this paper we consider the polynomial An(g) of degree n interpolating the coeecients. We show how An can be viewed as an inverse to the Bernstein polynomial operator and that the derivatives An(g) (r) converge uniformly to g (r) at the rate 1=n for all r. We also give an asymptotic expansion of Voronovskaya type for An(g) and discuss some shape preserving properties of this polynomial.
منابع مشابه
The eccentric connectivity index of bucket recursive trees
If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.
متن کاملPartial Convergence of Coupled Time-varying Systems
Asymptotic behavior of a partial state of coupled nonautonomous ordinary and/or partial differential equations is investigated. The system assumes the existence and uniqueness of the solution and the existence of a Lyapunov function candidate. Although ordinary Lyapunov analysis can not guarantee the asymptotic convergence of the state, the analysis in this paper assures the asymptotic converge...
متن کاملAsymptotic Approximation of the Move-To-Front Search Cost Distribution and Least-Recently-Used Caching Fault Probabilities
Limits and rate of convergence for the distribution of search cost under the move-to-front rule. I 2 (t) = Z log(t) 1 e ?x x (log(t=x)) d dx + Z t log t e ?x x (log(t=x)) d dx def = I 21 (t) + I 22 (t) (7.66) Here, the asymptotic behavior of I 21 (t) is determined by I 21 (t) (log(t)) d Z log(t) 1 e ?x x dx (log(t)) d Z 1 1 e ?x x dx; (7.67) and I 21 (t) (log(t= log(t))) d Z log(t) 1 e ?x x dx ...
متن کاملNonlinear Econometric Models with Cointegrated and Deterministically Trending Regressors1
This paper develops an asymptotic theory for a general class of nonlinear nonstationary regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares estimator. The estimator is consistent under fairly general conditions but the convergen...
متن کاملScattering Spaces and a Decomposition of Continuous Spectral Subspace of N - body Quantum Systems
We introduce the notion of scattering space S b for N-body quantum mechanical systems, where b is a cluster decomposition with 2 ≤ |b| ≤ N and r is a real number 0 ≤ r ≤ 1. Utilizing these spaces, we give a decomposition of continuous spectral subspace by S b for N-body quantum systems with long-range pair potentials V L α (xα) = O(|xα| ). This is extended to a decomposition by S b with 0 ≤ r ≤...
متن کامل