scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
TL;DR: This work considers a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods and shows that the positive definiteness of the generalized Hessian of the objective function in these inner problems is equivalent to the constraint nondegeneracy of the corresponding dual problems.
Abstract: We consider a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods. In order to analyze the rate of convergence of our proposed method, we characterize the Lipschitz continuity of the corresponding solution mapping at the origin. For the inner problems, we show that the positive definiteness of the generalized Hessian of the objective function in these inner problems, a key property for ensuring the efficiency of using an inexact semismooth Newton-CG method to solve the inner problems, is equivalent to the constraint nondegeneracy of the corresponding dual problems. Numerical experiments on a variety of large-scale SDP problems with the matrix dimension $n$ up to $4,110$ and the number of equality constraints $m$ up to $2,156,544$ show that the proposed method is very efficient. We are also able to solve the SDP problem fap36 (with $n=4,110$ and $m=1,154,467$) in the Seventh DIMACS Implementation Challenge much more accurately than in previous attempts.

392 citations

ReportDOI
TL;DR: In this paper, the authors provided an upper bound estimate of the rate of convergence to purchasing power parity using a panel of 51 prices from 48 cities in the United States, and found that convergence rates substantially higher than typically found in cross-country data.
Abstract: Using a panel of 51 prices from 48 cities in the United States, we provide an upper bound estimate of the rate of convergence to purchasing power parity. We find convergence rates substantially higher than typically found in cross-country data. We investigate some potentially serious biases induced by i.i.d. measurement errors in the data, and find our estimates to be robust to these potential biases. We also present evidence that convergence occurs faster for larger price differences. Finally, we find that rates of convergence are slower for cities farther apart. However, our estimates suggest that distance alone can only account for a small portion of the much slower convergence rates across national borders.

390 citations

Book ChapterDOI
01 Jan 1998
TL;DR: A discrete technique of the Schwarz alternating method is presented, to combine the Ritz-Galerkin and finite element methods, well suited for solving singularity problems in parallel.
Abstract: A discrete technique of the Schwarz alternating method is presented in this last chapter, to combine the Ritz-Galerkin and finite element methods. This technique is well suited for solving singularity problems in parallel, and requires a little more computation for large overlap of subdomains. The convergence rate of the iterative procedure, which depends upon overlap of subdomains, will be studied. Also a balance strategy will be proposed to couple the iteration number with the element size used in the FEM. For the crack-infinity problem of singularity the total CPU time by the technique in this chapter is much less than that by the nonconforming combination in Chapter 12.

389 citations

Journal ArticleDOI
TL;DR: The convergence rate for difference approximations to mixed initial boundary value problems has been shown to be linear in the convergence rate of the difference approximation as mentioned in this paper, which is the best known convergence rate.
Abstract: The convergence rate for difference approximations to mixed initial boundary value problems

386 citations

Journal ArticleDOI
01 Mar 1996
TL;DR: An algorithm for iterative learning control is proposed based on an optimisation principle used by other authors to derive gradient-type algorithms and has potential benefits which include realisation in terms of Riccati feedback and feedforward components.
Abstract: An algorithm for iterative learning control is proposed based on an optimisation principle used by other authors to derive gradient-type algorithms. The new algorithm is a descent algorithm and has potential benefits which include realisation in terms of Riccati feedback and feedforward components. This realisation also has the advantage of implicitly ensuring automatic step-size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm achieves a geometric rate of convergence for invertible plants. One important feature of the proposed algorithm is the dependence of the speed of convergence on weight parameters appearing in the norms of the signals chosen for the optimisation problem.

386 citations


Network Information
Related Topics (5)
Partial differential equation
70.8K papers, 1.6M citations
89% related
Markov chain
51.9K papers, 1.3M citations
88% related
Optimization problem
96.4K papers, 2.1M citations
88% related
Differential equation
88K papers, 2M citations
88% related
Nonlinear system
208.1K papers, 4M citations
88% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
2023693
20221,530
20212,129
20202,036
20191,995