Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning thi...Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.展开更多
Nonlinear m-term approximation plays an important role in machine learning, signal processing and statistical estimating. In this paper by means of a nondecreasing dominated function, a greedy adaptive compression num...Nonlinear m-term approximation plays an important role in machine learning, signal processing and statistical estimating. In this paper by means of a nondecreasing dominated function, a greedy adaptive compression numerical algorithm in the best m -term approximation with regard to tensor product wavelet-type basis is pro-posed. The algorithm provides the asymptotically optimal approximation for the class of periodic functions with mixed Besov smoothness in the L q norm. Moreover, it depends only on the expansion of function f by tensor pro-duct wavelet-type basis, but neither on q nor on any special features of f.展开更多
In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sid...In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sided approximation by the trigonometric polynomials on some classes of Besov spaces in the metricLp(Td(1≤p≤∞ are given.展开更多
针对阵列信号处理领域中的超分辨子空间类算法需计算阵列输出的协方差、协方差矩阵的特征分解及进行谱峰搜索得到波达方向(Direction of Arrival,DOA)估计,计算量较大则实际应用可能受限,提出了一种低计算复杂度的新颖的无需谱峰搜索的...针对阵列信号处理领域中的超分辨子空间类算法需计算阵列输出的协方差、协方差矩阵的特征分解及进行谱峰搜索得到波达方向(Direction of Arrival,DOA)估计,计算量较大则实际应用可能受限,提出了一种低计算复杂度的新颖的无需谱峰搜索的DOA估计算法。通过Nyström方法得到逼近的信号子空间,避免了直接对所有阵列输出计算协方差及对其特征分解从而降低了运算量。通过逼近的信号子空间构建低阶的关于DOA的特征多项式方程,对此低阶多项式方程求根得到DOA估计进一步降低了运算量,且不同于现有的DOA估计求根算法。理论分析和仿真结果表明,所提算法有着良好的估计精度及较低的计算复杂度。展开更多
Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . W...Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . We show that if the sequence πβ,fn,m , n∈Λ , ∧∈n,k are uniformly distributed on with respect to u as n∈Λ . Furthermore, a result about the behavior of the zeros of the exact maximally convergent sequence Λ is provided, under the condition that Λ is “dense enough”.展开更多
In this paper, K-controllability and approximate K-controllability of non- linear neutral differential equations in Banach spaces are studied. Sufficient conditions are established for each of these types of controlla...In this paper, K-controllability and approximate K-controllability of non- linear neutral differential equations in Banach spaces are studied. Sufficient conditions are established for each of these types of controllability. The results are obtained by using Leray-Schauder theory.展开更多
基金supported in part by the National Natural Science Foundation of China under Grants No.62027803,No.61601096,No.61971111,and No.61801089in part by the Science and Technology Program under Grants No.8091C24,No.2021JCJQJJ0949,and No.2022JCJQJJ0784in part by the Industrial Technology Development Program under Grant No.2020110C041.
文摘Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.
基金Supported by National Natural Science Foundation of China (No. 60872161, 10501026, 60675010 and 10626029)Natural Science Foundation of Tianjin (No. 08JCYBJC09600)China Postdoctoral Science Foundation ( No. 20070420708).
文摘Nonlinear m-term approximation plays an important role in machine learning, signal processing and statistical estimating. In this paper by means of a nondecreasing dominated function, a greedy adaptive compression numerical algorithm in the best m -term approximation with regard to tensor product wavelet-type basis is pro-posed. The algorithm provides the asymptotically optimal approximation for the class of periodic functions with mixed Besov smoothness in the L q norm. Moreover, it depends only on the expansion of function f by tensor pro-duct wavelet-type basis, but neither on q nor on any special features of f.
文摘In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sided approximation by the trigonometric polynomials on some classes of Besov spaces in the metricLp(Td(1≤p≤∞ are given.
基金Supported by Projects from NSF of China(10571147)Specialized Research Fund for Doctoral Programof Higher Education of China(20094301110001)+1 种基金NSF of Hunan Province (09JJ3002)Hunan Provincial Innovation Foundation for Postgraduate(S2008yjscx02)
文摘针对阵列信号处理领域中的超分辨子空间类算法需计算阵列输出的协方差、协方差矩阵的特征分解及进行谱峰搜索得到波达方向(Direction of Arrival,DOA)估计,计算量较大则实际应用可能受限,提出了一种低计算复杂度的新颖的无需谱峰搜索的DOA估计算法。通过Nyström方法得到逼近的信号子空间,避免了直接对所有阵列输出计算协方差及对其特征分解从而降低了运算量。通过逼近的信号子空间构建低阶的关于DOA的特征多项式方程,对此低阶多项式方程求根得到DOA估计进一步降低了运算量,且不同于现有的DOA估计求根算法。理论分析和仿真结果表明,所提算法有着良好的估计精度及较低的计算复杂度。
文摘Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let πβ,fn,m be the associated multipoint β-Padé approximant of order (n,m) . We show that if the sequence πβ,fn,m , n∈Λ , ∧∈n,k are uniformly distributed on with respect to u as n∈Λ . Furthermore, a result about the behavior of the zeros of the exact maximally convergent sequence Λ is provided, under the condition that Λ is “dense enough”.
基金The Young Scholar Foundation of Institute of Mathematics of Jilin University
文摘In this paper, K-controllability and approximate K-controllability of non- linear neutral differential equations in Banach spaces are studied. Sufficient conditions are established for each of these types of controllability. The results are obtained by using Leray-Schauder theory.
