The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to p...The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis.The obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.展开更多
A new unique common fixed point result for a pair of mappings satisfying certain quasi-Lipschitz type conditions on a topological vector space-valued cone metric space is obtained, and its particular forms and a more ...A new unique common fixed point result for a pair of mappings satisfying certain quasi-Lipschitz type conditions on a topological vector space-valued cone metric space is obtained, and its particular forms and a more general form are given. Our main results generalize and improve some well-known recent results in the literature.展开更多
In this paper we study the following nonlinear BSDE：y（t） ＋ ∫1 t f（s,y（s）,z（s））ds ＋ ∫1 t [z（s） ＋ g 1 （s,y（s）） ＋ εg 2 （s,y（s）,z（s））]dW s=ξ,t ∈ [0,1],where ε is a small parameter.The coeffi...In this paper we study the following nonlinear BSDE：y（t） ＋ ∫1 t f（s,y（s）,z（s））ds ＋ ∫1 t [z（s） ＋ g 1 （s,y（s）） ＋ εg 2 （s,y（s）,z（s））]dW s=ξ,t ∈ [0,1],where ε is a small parameter.The coefficient f is locally Lipschitz in y and z,the coefficient g 1 is locally Lipschitz in y,and the coefficient g 2 is uniformly Lipschitz in y and z.Let L N be the locally Lipschitz constant of the coefficients on the ball B（0,N） of R d × R d×r.We prove the existence and uniqueness of the solution when L N ～ √ log N and the parameter ε is small.展开更多
There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA...There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA) estimation system based on self-organizing map (SOM) and designed for arbitrarily distributed sensor array is proposed. The essential principle of this method is that the map from distance difference of arrival (DDOA) to DOA is Lipschitz continuity, it indicates the similar topology between them, and thus Kohonen SOM is a suitable network to classify DOA through DDOA. The simulation results show that the DOA estimation errors are less than 1° for most signals between 0° to 180°. Compared to MUSIC, Root-MUSIC, ESPRIT, and RBF, the errors of signals under signal-to-noise ratios (SNR) declines from 20 dB to 2 dB are robust, SOM is better than RBF and almost close to MUSIC. Further, the network can be trained in advance, which makes it possible to be implemented in real-time.展开更多
文摘The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis.The obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.
基金Supported by the National Natural Science Foundation of China(11361064)
文摘A new unique common fixed point result for a pair of mappings satisfying certain quasi-Lipschitz type conditions on a topological vector space-valued cone metric space is obtained, and its particular forms and a more general form are given. Our main results generalize and improve some well-known recent results in the literature.
文摘In this paper we study the following nonlinear BSDE：y（t） ＋ ∫1 t f（s,y（s）,z（s））ds ＋ ∫1 t [z（s） ＋ g 1 （s,y（s）） ＋ εg 2 （s,y（s）,z（s））]dW s=ξ,t ∈ [0,1],where ε is a small parameter.The coefficient f is locally Lipschitz in y and z,the coefficient g 1 is locally Lipschitz in y,and the coefficient g 2 is uniformly Lipschitz in y and z.Let L N be the locally Lipschitz constant of the coefficients on the ball B（0,N） of R d × R d×r.We prove the existence and uniqueness of the solution when L N ～ √ log N and the parameter ε is small.
文摘There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA) estimation system based on self-organizing map (SOM) and designed for arbitrarily distributed sensor array is proposed. The essential principle of this method is that the map from distance difference of arrival (DDOA) to DOA is Lipschitz continuity, it indicates the similar topology between them, and thus Kohonen SOM is a suitable network to classify DOA through DDOA. The simulation results show that the DOA estimation errors are less than 1° for most signals between 0° to 180°. Compared to MUSIC, Root-MUSIC, ESPRIT, and RBF, the errors of signals under signal-to-noise ratios (SNR) declines from 20 dB to 2 dB are robust, SOM is better than RBF and almost close to MUSIC. Further, the network can be trained in advance, which makes it possible to be implemented in real-time.
基金Supported by the National Nature Science Foundation of China(61174065)the Jiangsu Provincial Department of Education(10KJB20002)+1 种基金Nature Science Foundation at Nantong University(11Z05511Z056)
基金Supported by National Basic Research Program of China(973 Program2007CB814901)+1 种基金National Natural Science Foundation of China(10826098)Anhui Natural Science Foundation (090416225)
基金Research supported by the National Natural Science Foundation of China(10671168)Jiangsu Province(BK2006032)+2 种基金Educa-tion Department of Jiangsu Province(05KJD110220)Xuzhou Normal University(05PYL02)the Foundation of"Liu Da Ren Cai"Plan
