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 proved various sublinear global convergence rate results for the two classes of PMM based decomposition algorithms for function values and constraints violation and convergence of the sequences produced by the two algorithm classes to optimal primal-dual solutions.
Abstract: This paper presents two classes of decomposition algorithms based on the proximal method of multipliers (PMM) introduced in the mid-1970s by Rockafellar for convex minimization. We first show that ...
175 citations
Book•
23 Jan 2014
TL;DR: This paper presents preliminary results on rate of Convergence for Functions of BV/Bounded Functions on Bezier Variants, and some more results on Rate of convergence in Simultaneous Approximation.
Abstract: 1. Preliminaries.- 2. Approximation by Certain Operators.- 3. Complete Asymptotic Expansion.- 4. Linear and Iterative Combinations.- 5. Better Approximation.- 6. Complex Operators in Compact Disks.- 7. Rate of Convergence for Functions of BV.- 8. Convergence for BV/Bounded Functions on Bezier Variants.- 9. Some More Results on Rate of Convergence.- 10. Rate of Convergence in Simultaneous Approximation.- 11. Future Scope and Open Problems.
175 citations
TL;DR: An implicit algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier–Stokes equations is presented, constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system.
174 citations
TL;DR: Numerical experiments for a model elliptic singular perturbation problem show good agreement with the convergence estimates, even when few degrees of freedom are used and when d is as small as 10 -8 .
Abstract: We study the uniform approximation of boundary layer functions exp(-x/d) for x ∈ (0,1), d ∈ (0,1], by the p and hp versions of the finite element method. For the p version (with fixed mesh), we prove super-exponential convergence in the range p + 1/2 > e/(2d). We also establish, for this version, an overall convergence rate of O(p -1 √ln p) in the energy norm error which is uniform in d, and show that this rate is sharp (up to the √ln p term) when robust estimates uniform in d ∈ (0,1] are considered. For the p version with variable mesh (i.e., the hp version), we show that exponential convergence, uniform in d ∈ (0,1], is achieved by taking the first element at the boundary layer to be of size O(pd). Numerical experiments for a model elliptic singular perturbation problem show good agreement with our convergence estimates, even when few degrees of freedom are used and when d is as small as, e.g., 10 -8 . They also illustrate the superiority of the hp approach over other methods, including a low-order h version with optimal exponential mesh refinement. The estimates established in this paper are also applicable in the context of corresponding spectral element methods.
174 citations
TL;DR: It is demonstrated that the normalized least mean square (NLMS) algorithm can be viewed as a modification of the widely used LMS algorithm and is shown to have an important advantage over the LMS, which is that its convergence is independent of environmental changes.
Abstract: It is demonstrated that the normalized least mean square (NLMS) algorithm can be viewed as a modification of the widely used LMS algorithm. The NLMS is shown to have an important advantage over the LMS, which is that its convergence is independent of environmental changes. In addition, the authors present a comprehensive study of the first and second-order behavior in the NLMS algorithm. They show that the NLMS algorithm exhibits significant improvement over the LMS algorithm in convergence rate, while its steady-state performance is considerably worse. >
174 citations