Topic
Rate of convergence
About: Rate of convergence is a research topic. Over the lifetime, 31257 publications have been published within this topic receiving 795334 citations. The topic is also known as: convergence rate.
Papers published on a yearly basis
Papers
More filters
TL;DR: Under certain regularity conditions on the transition and reset kernels governing the dynamics of the stochastic hybrid system, the invariance probability computed using the approximating Markov chain is shown to converge to the invariant probability of the original stochastics hybrid system as the grid used in the approximation gets finer.
190 citations
09 Sep 2001
TL;DR: Convergence rate, widely used in the arena of the finite element method for evaluating new element’s performance, was exploited in this vehicle impact example.
Abstract: Response surface methods or metamodels are commonly used to approximate large computationally expensive engineering systems. Five response surface methods are studied: Stepwise Regression, Moving Least Square, Kriging, Multiquadric, and Adaptive and Interactive Modeling System. A real-world frontal impact design problem is used as an example, which is a complex, highly nonlinear, transient, dynamic, large deformation finite element model. To study the accuracy of the metamodel, the optimal Latin Hypercube Sampling method is used to distribute the sampling points uniformly over the entire design space. The Root Mean Square Error (RMSE) is used as the error indicator. Convergence rate, widely used in the arena of the finite element method for evaluating new element’s performance, was exploited in this vehicle impact example.
190 citations
TL;DR: This paper proposes a new structure and a new formulation for adapting the filter coefficients based on polyphase decomposition of the filter to be adapted and is independent of the type of filter banks used in the subband decomposition.
Abstract: Subband adaptive filtering has attracted much attention lately. In this paper, we propose a new structure and a new formulation for adapting the filter coefficients. This structure is based on polyphase decomposition of the filter to be adapted and is independent of the type of filter banks used in the subband decomposition. The new formulation yields improved convergence rate when the LMS algorithm is used for coefficient adaptation. As we increase the number of bands in the filter, the convergence rate increases and approaches the rate that can be obtained with a flat input spectrum. The computational complexity of the proposed scheme is nearly the same as that of the fullband approach. Simulation results are included to demonstrate the efficacy of the new approach.
190 citations
TL;DR: The /spl mu/-law PNLMS (MPNLMS) algorithm is proposed to keep, in contrast to the proportionate normalized least-mean-square (PNLMS), the fast initial convergence during the whole adaptation process in the case of sparse echo path identification.
Abstract: By analyzing the coefficient adaptation process of the steepest descent algorithm, the condition under which the fastest overall convergence will be achieved is obtained and the way to calculate optimal step-size control factors to satisfy that condition is formulated. Motivated by the results and using the stochastic approximation paradigm, the /spl mu/-law PNLMS (MPNLMS) algorithm is proposed to keep, in contrast to the proportionate normalized least-mean-square (PNLMS) algorithm, the fast initial convergence during the whole adaptation process in the case of sparse echo path identification. Modifications of the MPNLMS algorithm are proposed to lower the computational complexity.
190 citations
TL;DR: In this article, a comparison of nonparametric regression curves is considered, where the authors assume that there are parametric transformations of the axes which map one curve into the other.
Abstract: The comparison of nonparametric regression curves is considered. It is assumed that there are parametric (possibly nonlinear) transformations of the axes which map one curve into the other. Estimation and testing of the parameters in the transformations are studied. The rate of convergence is $n^{-1/2}$ although the nonparametric components of the model typically have a rate slower than that. A statistic is provided for testing the validity of a given completely parametric model.
190 citations