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: In this paper, it was shown that lifting and semidefinite relaxation suffice by themselves for stable recovery in the setting of m = O(nlogn) random sensing vectors, with high probability.
Abstract: We address the problem of recovering an n-vector from m linear measurements lacking sign or phase information. We show that lifting and semidefinite relaxation suffice by themselves for stable recovery in the setting of m=O(nlogn) random sensing vectors, with high probability. The recovery method is optimizationless in the sense that trace minimization in the PhaseLift procedure is unnecessary. That is, PhaseLift reduces to a feasibility problem. The optimizationless perspective allows for a Douglas-Rachford numerical algorithm that is unavailable for PhaseLift. This method exhibits linear convergence with a favorable convergence rate and without any parameter tuning.
139 citations
TL;DR: In this paper, it was shown that if the trial space is complete through polynomials of degreek?1, then it contains a functionv h such that |u?v h | s?ch k?s|u| k.
Abstract: The rate of convergence of the finite element method depends on the order to which the solutionu can be approximated by the trial space of piecewise polynomials. We attempt to unify the many published estimates, by proving that if the trial space is complete through polynomials of degreek?1, then it contains a functionv h such that |u?v h | s ?ch k?s|u| k . The derivatives of orders andk are measured either in the maximum norm or in the mean-square norm, and the estimate can be made local: the error in a given element depends on the diameterh i of that element. The proof applies to domains Ω in any number of dimensions, and employs a uniformity assumption which avoids degenerate element shapes.
138 citations
138 citations
TL;DR: An efficient and numerically stable implementation of a known algorithm is suggested for finding the extremal positive definite solutions of the matrix equation $X+A^*X^{-1}A=I$, if such solutions exist.
Abstract: An efficient and numerically stable implementation of a known algorithm is suggested for finding the extremal positive definite solutions of the matrix equation $X+A^*X^{-1}A=I$, if such solutions exist. The convergence rate is analyzed. A new algorithm that avoids matrix inversion is presented. Numerical examples are given to illustrate the effectiveness of the algorithms.
138 citations
01 Oct 1989
TL;DR: In this paper, it was shown that if the objective function is sufficiently smooth, the convergence rate can be made arbitrarily close to n-1/2 in the number of observations required.
Abstract: In this paper, we discuss some research issues related to the general topic of optimizing a stochastic system via simulation. In particular, we devote extensive attention to finite-difference estimators of objective function gradients and present a number of new limit theorems. We also discuss a new family of orthogonal function approximations to the global behavior of the objective function. We show that if the objective function is sufficiently smooth, the convergence rate can be made arbitrarily close to n-1/2 in the number of observations required. The paper concludes with a brief discussion of how these ideas can be integrated into an optimization algorithm.
138 citations