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: It is found that SFEM achieves more accurate results and higher convergence rates as compared with the corresponding finite elements in solving dynamic problems without increasing the computational cost.
171 citations
TL;DR: For uniformly ergodic Markov chains, this paper derived sensitivity bounds in terms of the ergodicity coefficient of the iterated transition kernel, which improved upon the bounds obtained by other authors.
Abstract: For uniformly ergodic Markov chains, we obtain new perturbation bounds which relate the sensitivity of the chain under perturbation to its rate of convergence to stationarity. In particular, we derive sensitivity bounds in terms of the ergodicity coefficient of the iterated transition kernel, which improve upon the bounds obtained by other authors. We discuss convergence bounds that hold in the case of finite state space, and consider numerical examples to compare the accuracy of different perturbation bounds.
171 citations
TL;DR: In this article, a stability and convergence analysis of sequential methods for coupled flow and geomechanics is presented, in which the mechanics sub-problem is solved first and the stability depends only on the coupling strength, independent of time step size.
170 citations
Book•
28 Aug 2011TL;DR: In this paper, the authors consider the formulation and local analysis of various quadratically convergent methods for solving the symmetric matrix inverse eigenvalue problem and give a general convergence analysis, which covers both the distinct and the multiple eigen value cases.
Abstract: We consider the formulation and local analysis of various quadratically convergent methods for solving the symmetric matrix inverse eigenvalue problem. One of these methods is new. We study the case where multiple eigenvalues are given: we show how to state the problem so that it is not overdetermined, and describe how to modify the numerical methods to retain quadratic convergence on the modified problem. We give a general convergence analysis, which covers both the distinct and the multiple eigenvalue cases. We also present numerical experiments which illustrate our results.
170 citations
TL;DR: In this article, the authors considered a continuous idealization of the PET reconstruction problem, considered as an example of bivariate density estimation based on indirect observations, and established exact minimax rates of convergence of estimation, for all possible estimators, over suitable smoothness classes of functions.
Abstract: Several algorithms for image reconstruction in positron emission tomography (PET) have been described in the medical and statistical literature. We study a continuous idealization of the PET reconstruction problem, considered as an example of bivariate density estimation based on indirect observations. Given a large sample of indirect observations, we consider the size of the equivalent sample of observations, whose original exact positions would allow equally accurate estimation of the image of interest. Both for indirect and for direct observations, we establish exact minimax rates of convergence of estimation, for all possible estimators, over suitable smoothness classes of functions. A key technical device is a modulus of continuity appropriate to global function estimation. For indirect data and (in practice unobservable) direct data, the rates for mean integrated square error are $n^{-p/(p + 2)}$ and $(n/\log n)^{-p/(p + 1)}$, respectively, for densities in a class corresponding to bounded square-integrable $p$th derivatives. We obtain numerical values for equivalent sample sizes for minimax linear estimators using a slightly modified error criterion. Modifications of the model to incorporate attenuation and the third dimension effect do not affect the minimax rates. The approach of the paper is applicable to a wide class of linear inverse problems.
170 citations