With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued no...With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.展开更多
In this paper, a local multilevel product algorithm and its additive version are con- sidered for linear systems arising from adaptive nonconforming P1 finite element approx- imations of second order elliptic boundary...In this paper, a local multilevel product algorithm and its additive version are con- sidered for linear systems arising from adaptive nonconforming P1 finite element approx- imations of second order elliptic boundary value problems. The abstract Schwarz theory is applied to analyze the multilevel methods with Jaeobi or Gauss-Seidel smoothers per- formed on local nodes on coarse meshes and global nodes on the finest mesh. It is shown that the local multilevel methods are optimal, i.e., the convergence rate of the multilevel methods is independent of the mesh sizes and mesh levels. Numerical experiments are given to confirm the theoretical results.展开更多
基金supported by the National Natural Science Foundation of China(6100115361271415+4 种基金6140149961531015)the Fundamental Research Funds for the Central Universities(3102014JCQ010103102014ZD0041)the Opening Research Foundation of State Key Laboratory of Underwater Information Processing and Control(9140C231002130C23085)
文摘With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.
基金Acknowledgements. The work of the first author was supported by the National Basic Research Program under the Grant 2011CB30971 and National Science Foundation of China （11171335）. The work of the second author was supported by the National Natural Science Foundation of China （Grant No. 11201394） and the Fundamental Research Funds for the Central Universities （Grant No. 2012121003）.
文摘In this paper, a local multilevel product algorithm and its additive version are con- sidered for linear systems arising from adaptive nonconforming P1 finite element approx- imations of second order elliptic boundary value problems. The abstract Schwarz theory is applied to analyze the multilevel methods with Jaeobi or Gauss-Seidel smoothers per- formed on local nodes on coarse meshes and global nodes on the finest mesh. It is shown that the local multilevel methods are optimal, i.e., the convergence rate of the multilevel methods is independent of the mesh sizes and mesh levels. Numerical experiments are given to confirm the theoretical results.
