scholarly journals Topology design for distributed formation control towards optimal convergence rate

2012 ◽  
Author(s):  
Huang Huang ◽  
Changbin Yu ◽  
Azwirman Gusrialdi ◽  
Sandra Hirche
Keyword(s):  
Convergence Rate ◽  
Formation Control ◽  
Topology Design ◽  
Optimal Convergence Rate ◽  
Optimal Convergence

Reachability of Optimal Convergence Rate Estimates for High-Order Numerical Convex Optimization Methods

2019 ◽  
Vol 99 (1) ◽  
pp. 91-94
Author(s):  
A. V. Gasnikov ◽  
E. A. Gorbunov ◽  
D. A. Kovalev ◽  
A. A. M. Mokhammed ◽  
E. O. Chernousova
Keyword(s):  
Convex Optimization ◽  
Convergence Rate ◽  
Optimization Methods ◽  
High Order ◽  
Optimal Convergence Rate ◽  
Optimal Convergence

Trimmed estimators for large dimensional sparse covariance matrices

2018 ◽  
Vol 08 (01) ◽  
pp. 1950003
Author(s):  
Guangren Yang ◽  
Xia Cui
Keyword(s):  
Convergence Rate ◽  
Covariance Matrix ◽  
Covariance Matrices ◽  
Optimal Convergence Rate ◽  
Sample Covariance Matrices ◽  
Optimal Convergence ◽  
Sample Covariance ◽  
Starting Point ◽  
Pairwise Product

In this paper, we will propose two new estimators for sparse covariance matrix. Our starting point is to make the estimator of each element of covariance matrix more robust. More precisely, we will trim the observations for each pairwise product of components of population as a first step. Then we form the sample covariance matrices based on the trimmed data. Finally, we apply the thresholding to the derived sample covariance matrices. These two new estimators will be shown to achieve the optimal convergence rate.

Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method

2013 ◽  
Vol 51 (2) ◽  
pp. 1327-1348 ◽  
Author(s):  
M. Feischl ◽  
M. Karkulik ◽  
J. M. Melenk ◽  
D. Praetorius
Keyword(s):  
Boundary Element Method ◽  
Convergence Rate ◽  
Boundary Element ◽  
Optimal Convergence Rate ◽  
Optimal Convergence ◽  
Element Method

scholarly journals NUMERICAL ALGORITHM FOR SOLVING THE CONTINUATION PROBLEM FOR THE ACOUSTIC EQUATION

2020 ◽  
Vol 70 (2) ◽  
pp. 7-13
Author(s):  
J.A. Askerbekova ◽  
Keyword(s):  
Inverse Problem ◽  
Convergence Rate ◽  
Direct Problem ◽  
Natural Extension ◽  
Nonlinear Problems ◽  
Initial Boundary ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Optimal Convergence Rate ◽  
Optimal Convergence

In this paper we consider the initial-boundary value problem for the acoustics equation in the temporal-triangular domain. We reduce the original ill-posed problem to an equivalent inverse problem with respect to some direct problem. This direct problem is well-posed. The inverse problem is replaced by a minimization problem. An algorithm for solving the inverse problem by the Landweber iteration method is constructed. We apply the method of successive approximations to the equation, we obtain a natural extension to nonlinear problems. This method leads to optimal convergence rate in certain cases. An analysis of the iterative Landweber method for nonlinear problems depends on the source conditions and additional conditions. Convergence analysis and error estimates are usually made with many assumptions, which are very difficult to verify from a practical point of view. This method leads to optimal convergence rate under certain conditions. Theoretical analysis is confirmed by numerical results. Visual examples are processed numerically.

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