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.
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TL;DR: In this paper, a hybrid method combining the output-least-squares and the equation error method is proposed for the estimation of parameters in elliptic partial differential equations, which is realized by an augmented Lagrangian formulation, and convergence and rate of convergence proofs are provided.
Abstract: In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.
168 citations
TL;DR: A Walsh space is defined which contains all functions whose partial mixed derivatives up to order $\delta \ge 1$ exist and have finite variation and it is shown that quasi-Monte Carlo rules based on digital $(t,\alpha,s)$-sequences achieve the optimal rate of convergence of the worst-case error for numerical integration.
Abstract: We define a Walsh space which contains all functions whose partial mixed derivatives up to order $\delta \ge 1$ exist and have finite variation. In particular, for a suitable choice of parameters, this implies that certain Sobolev spaces are contained in these Walsh spaces. For this Walsh space we then show that quasi-Monte Carlo rules based on digital $(t,\alpha,s)$-sequences achieve the optimal rate of convergence of the worst-case error for numerical integration. This rate of convergence is also optimal for the subspace of smooth functions. Explicit constructions of digital $(t,\alpha,s)$-sequences are given, hence providing explicit quasi-Monte Carlo rules which achieve the optimal rate of convergence of the integration error for arbitrarily smooth functions.
168 citations
TL;DR: In this paper, the authors studied a discrete-time approximation for decoupled Forward-Backward Stochastic Differential Equations (FBSDEs) with jumps and proved the convergence of the scheme when the number of time steps n goes to infinity.
168 citations
TL;DR: The numerical results demonstrate that ADM–PADE (MADM-PADE) technique gives the approximate solution with faster convergence rate and higher accuracy than using ADM (M ADM).
168 citations
TL;DR: In this article, the authors show that the convergence test and the mean-reversion test are not equivalent and provide an empirical example in which the null hypothesis of no mean reversion is rejected but the null hypotheses of no convergence is not rejected.
Abstract: The authors show that, contrary to the beliefs of some previous analysts of international economic growth, the hypotheses of convergence and of mean-reversion are not equivalent. Under some assumptions, the rate of convergence is independent of the degree of mean-reversion; under other assumptions, mean-reversion is a necessary, but not a sufficient, condition for convergence. The authors show the relationship between the convergence test and the mean-reversion test and provide an empirical example in which the null hypothesis of no mean-reversion is rejected but the null hypothesis of no convergence is not rejected. Copyright 1994 by MIT Press.
167 citations