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A TRUST-REGION METHOD FOR SOLVING TRUNCATED COMPLEX SINGULAR VALUE DECOMPOSITION
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作者 Jiaofen Li Lingchang Kong +2 位作者 Xuefeng Duan Xuelin Zhou Qilun Luo 《Journal of Computational Mathematics》 SCIE CSCD 2024年第4期999-1031,共33页
The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is fo... The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et al.is presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence rate.Numerical experiments are provided to illustrate the efficiency of the proposed method.Comparisons with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach. 展开更多
关键词 Truncated singular value decomposition Riemannian optimization Trust-region method
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A Novel Method to Enhance the Inversion Speed and Precision of the NMR T_(2) Spectrum by the TSVD Based Linearized Bregman Iteration
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作者 Yiguo Chen Congjun Feng +4 位作者 Yonghong He Zhijun Chen Xiaowei Fan Chao Wang Xinmin Ge 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第9期2451-2463,共13页
The low-field nuclear magnetic resonance(NMR)technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields.However,the speed and accuracy of the ex... The low-field nuclear magnetic resonance(NMR)technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields.However,the speed and accuracy of the existing numerical inversion methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation and the contamination of the noises.This paper proposes a novel inversion algorithmto accelerate the convergence and enhance the precision using empirical truncated singular value decompositions(TSVD)and the linearized Bregman iteration.The L1 penalty term is applied to construct the objective function,and then the linearized Bregman iteration is utilized to obtain fast convergence.To reduce the complexity of the computation,empirical TSVD is proposed to compress the kernel matrix and determine the appropriate truncated position.This novel inversion method is validated using numerical simulations.The results indicate that the proposed novel method is significantly efficient and can achieve quick and effective data solutions with low signal-to-noise ratios. 展开更多
关键词 Low field nuclear magnetic resonance linearized bregman iteration truncated singular value decomposition numerical simulations
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INTERPOLATION OF HEAD-RELATED TRANSFER FUNCTIONS USING SPHERICAL FOURIER EXPANSION 被引量:1
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作者 Huang Qinghua Fang Yong 《Journal of Electronics(China)》 2009年第4期571-576,共6页
A new interpolation algorithm for Head-Related Transfer Function (HRTF) is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical ha... A new interpolation algorithm for Head-Related Transfer Function (HRTF) is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical harmonics on a spherical surface. Truncated Singular Value Decomposition (SVD) is adopted to calculate the weights of the model. The truncation number is chosen according to Frobenius norm ratio and the partial condition number. Compared with other interpolated methods, our proposed approach not only is continuous but exploits global information of available directions. The HRTF from any desired direction can be and interpolated results demonstrate that our obtained more accurately and robustly. Reconstructed proposed algorithm acquired better performance. 展开更多
关键词 Head-Related Transfer Function (HRTF) INTERPOLATION Spherical Fourier Expansion (SFE) Truncated singular value Decomposition (SVD) Partial condition number
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A Truncated SVD-Based ARIMA Model for Multiple QoS Prediction in Mobile Edge Computing 被引量:12
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作者 Chao Yan Yankun Zhang +2 位作者 Weiyi Zhong Can Zhang Baogui Xin 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2022年第2期315-324,共10页
In the mobile edge computing environments,Quality of Service(QoS)prediction plays a crucial role in web service recommendation.Because of distinct features of mobile edge computing,i.e.,the mobility of users and incom... In the mobile edge computing environments,Quality of Service(QoS)prediction plays a crucial role in web service recommendation.Because of distinct features of mobile edge computing,i.e.,the mobility of users and incomplete historical QoS data,traditional QoS prediction approaches may obtain less accurate results in the mobile edge computing environments.In this paper,we treat the historical QoS values at different time slots as a temporal sequence of QoS matrices.By incorporating the compressed matrices extracted from QoS matrices through truncated Singular Value Decomposition(SVD)with the classical ARIMA model,we extend the ARIMA model to predict multiple QoS values simultaneously and efficiently.Experimental results show that our proposed approach outperforms the other state-of-the-art approaches in accuracy and efficiency. 展开更多
关键词 edge computing QoS prediction Auto Regressive Integrated Moving Average(ARIMA) truncated singular value Decomposition(SVD)
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Inversion of vegetation height from Pol In SAR using complex least squares adjustment method 被引量:6
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作者 FU HaiQiang WANG ChangCheng +2 位作者 ZHU JianJun XIE QingHua ZHAO Rong 《Science China Earth Sciences》 SCIE EI CAS CSCD 2015年第6期1018-1031,共14页
In this paper, we propose the novel method of complex least squares adjustment (CLSA) to invert vegetation height accurately using single-baseline polarimetric synthetic aperture radar interferometry (PollnSAR) da... In this paper, we propose the novel method of complex least squares adjustment (CLSA) to invert vegetation height accurately using single-baseline polarimetric synthetic aperture radar interferometry (PollnSAR) data. CLSA basically estimates both volume-only coherence and ground phase directly without assuming that the ground-to-volume amplitude radio of a particular polarization channel (e.g., HV) is less than -10 dB, as in the three-stage method. In addition, CLSA can effectively limit errors in interferometric complex coherence, which may translate directly into erroneous ground-phase and volume-only coherence estimations. The proposed CLSA method is validated with BioSAR2008 P-band E-SAR and L-band SIR-C PollnSAR data. Its results are then compared with those of the traditional three-stage method and with external data. It implies that the CLSA method is much more robust than the three-stage method. 展开更多
关键词 polarimetric SAR interferometry (PolInSAR) complex least squares adjustment random volume over ground (RVoG) vegetation height inversion truncated singular value decomposition (T-SVD)
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A universal solution to one-dimensional oscillatory integrals 被引量:4
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作者 LI JianBing WANG XueSong WANG Tao 《Science in China(Series F)》 2008年第10期1614-1622,共9页
How to calculate the highly oscillatory integrals is the bottleneck that restraints the research of light wave and electromagnetic wave's propagation and scattering. Levin method is a classical quadrature method for ... How to calculate the highly oscillatory integrals is the bottleneck that restraints the research of light wave and electromagnetic wave's propagation and scattering. Levin method is a classical quadrature method for this type of integrals. Unfortunately it is susceptible to the system of linear equations' ill-conditioned behavior. We bring forward a universal quadrature method in this paper, which adopts Chebyshev differential matrix to solve the ordinary differential equation (ODE). This method can not only obtain the indefinite integral' function values directly, but also make the system of linear equations well-conditioned for general oscillatory integrals. Furthermore, even if the system of linear equations in our method is ill-conditioned, TSVD method can be adopted to solve them properly and eventually obtain accurate integral results, thus making a breakthrough in Levin method's susceptivity to the system of linear equations' ill-conditioned behavior. 展开更多
关键词 oscillatory integrals Levin method Chebyshev differential matrix ill-conditioned matrix Truncated singular value decomposition
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