To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the...To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.展开更多
This paper develops distributed algorithms for solving Sylvester equations.The authors transform solving Sylvester equations into a distributed optimization problem,unifying all eight standard distributed matrix struc...This paper develops distributed algorithms for solving Sylvester equations.The authors transform solving Sylvester equations into a distributed optimization problem,unifying all eight standard distributed matrix structures.Then the authors propose a distributed algorithm to find the least squares solution and achieve an explicit linear convergence rate.These results are obtained by carefully choosing the step-size of the algorithm,which requires particular information of data and Laplacian matrices.To avoid these centralized quantities,the authors further develop a distributed scaling technique by using local information only.As a result,the proposed distributed algorithm along with the distributed scaling design yields a universal method for solving Sylvester equations over a multi-agent network with the constant step-size freely chosen from configurable intervals.Finally,the authors provide three examples to illustrate the effectiveness of the proposed algorithms.展开更多
基金This work was supported in part by the National Fundamental Research Program(Grant No.G1998030406)the National Natural Science Foundation of China(Grant No.69972020)by the State Key Lab on Microwave and Digital Communications,Department of Electronics Engineering,Tsinghua University.
文摘To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.62103003,72171171,62073035,61973002in part by the Anhui Provincial Natural Science Foundation under Grant No.2008085J32。
文摘This paper develops distributed algorithms for solving Sylvester equations.The authors transform solving Sylvester equations into a distributed optimization problem,unifying all eight standard distributed matrix structures.Then the authors propose a distributed algorithm to find the least squares solution and achieve an explicit linear convergence rate.These results are obtained by carefully choosing the step-size of the algorithm,which requires particular information of data and Laplacian matrices.To avoid these centralized quantities,the authors further develop a distributed scaling technique by using local information only.As a result,the proposed distributed algorithm along with the distributed scaling design yields a universal method for solving Sylvester equations over a multi-agent network with the constant step-size freely chosen from configurable intervals.Finally,the authors provide three examples to illustrate the effectiveness of the proposed algorithms.
