On the rate of convergence of nearest neighbor rules (Corresp.)

An erroneous method for maximizing the projected divergence between two Gaussian multivariate hypotheses appeared in a recent paper. The correct solution is given.     

On the almost sure rate of convergence of linear stochastic approximation algorithms

The almost sure rate of convergence of linear stochastic approximation algorithms is analyzed. As the main result, it is demonstrated that their almost sure rate of convergence is equivalent to the almost sure rate of convergence of the averages of their input data sequences. As opposed to most of the existing results on the rate of convergence of stochastic approximation which cover only algorithms with the noise decomposable as the sum of a martingale difference, vanishing and telescoping sequence, the main results of this paper hold under assumptions not requiring the input data sequences to admit any particular decomposition. Although no decomposition of the input data sequences is required, the results on the almost sure rate of convergence of linear stochastic approximation algorithms obtained in this correspondence are as tight as the rate of convergence in the law of iterated logarithm. Moreover, the main result of this correspondence yields the law of iterated logarithm for linear stochastic approximation if the law of iterated logarithm holds for the input data sequences. The obtained general results are illustrated with two (nontrivial) examples where the input data sequences are strongly mixing strictly stationary random processes or functions of a uniformly ergodic Markov chain. These results are also applied to the analysis of least mean square (LMS) algorithms.     

基于随愿网络的运营商云网融合业务的研究与实现

随着云计算技术的发展和网络业务需求的增加,云网融合成为网络架构变革的必然选择。然而,云网融合时代的到来给传统网络运维带来了巨大的挑战,网络需要向更加智能和便捷的模式转变,目前被业界广泛研究的智能型通信网络——随愿网络,成为解决这一问题的最佳选择。阐述了随愿网络的发展过程、架构和关键步骤,并结合当前运营商云专网多云互联业务的现实需求,以云网融合的典型业务场景为例,分析了基于随愿网络的云网融合业务的实现过程,以期为随愿网络与云网融合业务的结合及实践提供参考。     

Adaptive controller yielding fast convergence rate

A way of improving the transient performance is suggested for a class of model reference adaptive control systems     

On the extreme eigenvalues of Toeplitz and real Hankel interval matrices

The purpose of this paper is to evaluate the extreme eigenvalues of a Hermitian Toeplitz interval matrix and a real Hankel interval matrix. A (n×n)-dimensional Hermitian Toeplitz (HT) matrix is determined by the elements of its first row, sayr. If the elements ofr lie in complex intervals (i.e., rectangles of the complex plane), we call the resulting set of matrices an HT interval (HTI) matrix. An HTI matrix can model real world HT matrices where the elements of the vectorr have finite precision (e.g., because of quantization, or imprecise measurement devices). In this paper we prove that the extreme eigenvalues of a given HTI matrix can be easily obtained from the 2^2(n–1) vertex HT matrices where the first element ofr is set to zero. Similarly, as a special case we obtain that the extreme eigenvalues of a real symmetric Toeplitz interval (RSTI) matrix can be obtained from 2 ^n–1 vertex matrices. Based on the above results we provide boxlike bounds for the eigenvalues on non-Hermitian complex and real Toeplitz interval matrices. Finally, we consider a real Hankel interval matrix. We prove that the maximal eigenvalue of a (n×n)-dimensional real Hankel interval matrix can be obtained from a subset of the vertex Hankel matrices containing 2^2n–3 vertex matrices, whereas the minimal eigenvalue can be obtained from another such subset also containing 2^2n–3 vertex matrices.     

Statistical analysis for the convergence rate of signals to medianfilter roots

The convergence behavior of the median filter is analyzed. A concept called convergence point is used to characterize the convergence rates. The results show that any independently and identically distributed (i.i.d) signal will become nearly stable after three or four passes of median filter with a large probability. Simulations are provided to illustrate the theoretical developments     

On the convergence properties of the Hopfield model

The main contribution of the present work is showing that the known convergence properties of the Hopfield model can be reduced to a very simple case, for which an elementary proof is provided. The convergence properties of the Hopfield model are dependent on the structure of the interconnections matrix W and the method by which the nodes are updated. Three cases are known: (1) convergence to a stable state when operating in a serial mode with symmetric W; (2) convergence to a cycle of length 2, at most, when operating in a fully parallel mode with symmetric W; and (3) convergence to a cycle of length 4 when operating in a fully parallel mode with antisymmetric W. The three known results are reviewed and it is proven that the fully parallel mode of operation is a special case of the serial model of operation. There are three more cases than can be considered using this characterization: serial mode of operation, antisymmetric W; serial mode of operation, arbitrary W; and fully parallel mode of operation, arbitrary W. By exhibiting exponential lower bounds on the length of the cycles in other cases, it is proven that the three known cases are the only interesting ones     

Study of convergence rate of Newton's procedure within harmonicbalance

Harmonic balance is studied. The traditional procedure, which involves the discrete Fourier transform (DFT), is compared to the boundary values approach. Presenting the problem using a simple expression, it is proved that both approaches have identical convergence. It is also suggested that DFT is numerically more expensive     

ON CONVERGENCE OF COLLOCATION TECHNIQUE

In this paper,the convergence rate at matching points of collocation technique isshown to be O(h~2),that is just the same as the global convergence rate of Galerkin's method withtriangular pulses as basis and weighting functions.A numerical example to verify the conclusionis given.     

On the convergence and roots of order-statistics filters

We propose a comprehensive theory of the convergence and characterization of roots of order-statistics filters. Conditions for the convergence of iterations of order-statistics filters are proposed. Criteria for the morphological characterization of roots of order-statistics filters are also proposed     

Generalization performance of regularization networks and supportvector machines via entropy numbers of compact operators

We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use of a viewpoint that is apparently novel in the field of statistical learning theory. The hypothesis class is described in terms of a linear operator mapping from a possibly infinite-dimensional unit ball in feature space into a finite-dimensional space. The covering numbers of the class are then determined via the entropy numbers of the operator. These numbers, which characterize the degree of compactness of the operator can be bounded in terms of the eigenvalues of an integral operator induced by the kernel function used by the machine. As a consequence, we are able to theoretically explain the effect of the choice of kernel function on the generalization performance of support vector machines     

On the convergence of the classical symmetrical condensed node-TLMscheme

This paper presents a proof of convergence of the transmission-line matrix (TLM) method with a symmetrical condensed node (SCN) in the classical formulation of Johns (1987). It is shown that the convergence order of the SCN-TLM method cannot simply be derived from observing the dispersion characteristics of the TLM mesh. The mapping between the discretized electromagnetic field and TLM wave amplitudes plays a decisive role. Although second-order convergence is observed for coarse discretizations, which are usually used in practice due to the limitations of memory resources, it is shown and numerically verified that the asymptotic convergence reduces to order 𝒪(√Δt). Only using a bijective field mapping defined at the cell boundaries yields second-order convergence     

Improving the convergence rate of the conjugate gradient FFT methodusing subdomain basis functions

A technique to improve the convergence rate of the conjugate gradient-fast Fourier transform (CG-FFT) method is presented. The procedure involves the incorporation of subdomain basis functions associated with the current representation of linear and planar radiating elements. It is shown that significant improvements are achieved in the convergence of the CG-FFT when using sinusoidal basis functions. Numerical results are presented for thin cylindrical dipoles, conducting strips, and material plates of various sizes. In all cases, an increase in the rate of convergence by a factor of two or better was observed     

On convergence of Lloyd's method I

Although Lloyd's method I for optimal quantization was proposed more than thirty years ago and has been frequently referred to in the literature, its convergence has so far not been shown. This correspondence proves that Lloyd's method I converges for a large class of error measures, if the density function is continuous, positive, and defined on a finite interval. The proof is done by modeling the behavior of a continuous optimization algorithm by a finite state machine     

Discrete constrained iterative deconvolution algorithms with optimized rate of convergence

In this paper, some new constrained discrete deconvolution algorithms based on an iterative equation are presented. The constraints are—the signal extent (signal support)—the positivity—the level bounds. The algorithms minimize either the error energy or a positive functional. The connections with previous works are studied. An experimental comparison of the algorithms convergence speed is studied with a synthetic sequence to be recovered. The restoration error and both the deconvoluted signal and its spectrum show clearly the performances of the algorithms and their ability to achieve a spectral extrapolation. The deconvolution from noisy data is investigated.     

Quantifying the effects of dimension on the convergence rate of theLMS adaptive FIR estimator

The convergence rate of an LMS adaptive FIR filter to an unknown stationary channel may be influenced by the filter parameter dimension as well as by the input signal's characteristics. This dimension influence may be of importance in applications, such as adaptive acoustic echo cancellation, in which the unknown channel is typically modeled as a “long” FIR filter. The paper includes the development and proposal of a novel measure of the expected convergence rate of the LMS/FIR filter followed by analysis of this convergence rate measure. The analysis indicates that unless the input signal is white, the expected convergence rate decreases with increasing dimension down to a limiting value, which is determined by the input signal's autocorrelation level     

On the convergence of discrimination information (Corresp.)

A sufficient condition involving a hypothesis of mean-square convergence is given for the convergence of discrimination information. A stronger condition requiring uniform convergence has already been given. An example is given which satisfies the mean-square convergence hypothesis but not the uniform convergence hypothesis.     

On the convergence of numerical results in modal analysis

Previous studies of the relative convergence (RC) phenomenon in modal analysis showed the need to introduce the edge condition by using an explicit asymptotic behavior of modal coefficients. We do not agree that the edge condition is the only means of uniquely defining a solution. It is demonstrated that the RC can be avoided by including only the bounded feature of modal coefficients. The analytical computations are given in solving the bifurcated parallel plate waveguide. To solve the general problem of convergence of numerical results, a-proof is given of this convergence in modal analysis. The required condition is the use of a "well-conditioned" linear system. With this demonstration, the use of the condition number as purely numerical criterion is justified to ensure the convergence of results.     

On the convergence of real-time active noise control systems

Available convergence analyses of adaptive active noise control systems apply to only theoretical cases with broad-band white noise or pure delay secondary paths. In order to investigate convergence behaviors of these systems in more practical conditions, this paper conducts a new convergence analysis for filtered-x LMS-based active noise control systems with band-limited white noise and moving average secondary paths. A linear model for the adaptation process is developed. Based on this model, the upper-bound of the adaptation step-size is derived. Also, the adaptation step-size leading to the fastest convergence rate is derived. In addition to the computer simulation, a fully implemented real time active noise control system is used to verify the validity of the analytical results.