Henrici's transformation is the underlying scheme that generates, by cycling, Steffensen's method for the approximation of the solution of a nonlinear equation in several variables. The aim of this paper is to analyze the asymptotic behavior of the obtained sequence (sn*
) by applying Henrici's transformation when the initial sequence (sn) behaves sublinearly. We extend the work done in the regular case by Sadok [17] to vector sequences in the singular case. Under suitable conditions, we show that the slowest convergence rate of (sn*
) is to be expected in a certain subspace N of Rp. More precisely, if we write sn*
=sn*
,N+sn*
,N, the orthogonal decomposition into N and N, then the convergence is linear for (sn*
,N) but (
n*
,N) converges to the same limit faster than the initial one. In certain cases, we can have N=Rp and the convergence is linear everywhere. 相似文献
We study quasi-Monte Carlo algorithms based on low discrepancy sequences for multivariate integration. We consider the problem of how the minimal number of function evaluations needed to reduce the worst-case error from its initial error by a factor of depends on and the dimension . Strong tractability means that it does not depend on and is bounded by a polynomial in . The least possible value of the power of is called the -exponent of strong tractability. Sloan and Wozniakowski established a necessary and sufficient condition of strong tractability in weighted Sobolev spaces, and showed that the -exponent of strong tractability is between 1 and 2. However, their proof is not constructive.
In this paper we prove in a constructive way that multivariate integration in some weighted Sobolev spaces is strongly tractable with -exponent equal to 1, which is the best possible value under a stronger assumption than Sloan and Wozniakowski's assumption. We show that quasi-Monte Carlo algorithms using Niederreiter's -sequences and Sobol sequences achieve the optimal convergence order for any 0$"> independent of the dimension with a worst case deterministic guarantee (where is the number of function evaluations). This implies that strong tractability with the best -exponent can be achieved in appropriate weighted Sobolev spaces by using Niederreiter's -sequences and Sobol sequences.
To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. A new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-order (at least) 1 by showing the existence of a unique real number q [1,+] such that either exact Q-order, exact Q-superorder, or exact Q-suborder q of convergence holds.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
Let be Singer's invariant-theoretic model of the dual of the lambda algebra with , where denotes the mod 2 Steenrod algebra. We prove that the inclusion of the Dickson algebra, , into is a chain-level representation of the Lannes-Zarati dual homomorphism
The Lannes-Zarati homomorphisms themselves, , correspond to an associated graded of the Hurewicz map
Based on this result, we discuss some algebraic versions of the classical conjecture on spherical classes, which states that Only Hopf invariant one and Kervaire invariant one classes are detected by the Hurewicz homomorphism. One of these algebraic conjectures predicts that every Dickson element, i.e. element in , of positive degree represents the homology class in for 2$">.
We also show that factors through , where denotes the differential of . Therefore, the problem of determining should be of interest.
Suppose that { f(n), n N0} is a sequence of positive real numbers and suppose that the sequence { a(n), n N0} is given by a(0) = 0, and, for n 1, by the convolution equation nf(n) = a* f(n). The resulting sequence is denoted by a(n) = f(n) and is called the De Pril transform of { f(n), n N0} . In this paper, we consider first- and second-order asymptotic behavior of { f(n), n N0} for a large class of subexponential sequences { f(n), n N0} . We also discuss some applications. 相似文献
In this paper, we give necessary and sufficient conditions for infinite matrices mapping from the Nakano vector-valued sequence space (X, p) into any BK-space, and by using this result, we obtain the matrix characterizations from (X, p) into the sequence spaces (Y), c0(Y, q), c(Y), s(Y), Er(Y), and Fr(Y), where p = (pk) and q = (qk) are bounded sequences of positive real numbers such that pk 1 for all kN, r 0, and s 1.AMS Subject Classification (2000): 46A45 相似文献
The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem. 相似文献
We study rate of convergence in the strong law of large numbers for finite and infinite variance time series in both contexts of weak and strong dependence. 相似文献