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
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
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
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
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
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
基金supported by the National Natural Science Foundation of China(Grant Nos.12261026,11961012,12201149)by the Natural Science Foundation of Guangxi Province(Grant Nos.2016GXNSFAA380074,2023GXNSFAA026067)+4 种基金by the Innovation Project of GUET Graduate Education(Grant No.2022YXW01)by the GUET Graduate Innovation Project(Grant No.2022YCXS142)by the Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(Grant Nos.YQ23103,YQ21103,YQ22106)by the Special Fund for Science and Technological Bases and Talents of Guangxi(Grant No.2021AC06001)by the Guizhou Science and Technology Program of Projects(Grant No.ZK2021G339)。
文摘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.
基金support by the National Nature Science Foundation of China(42174142)CNPC Innovation Found(2021DQ02-0402)National Key Foundation for Exploring Scientific Instrument of China(2013YQ170463).
文摘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.
基金Supported by Shanghai Natural Science Foundation, Shanghai Leading Academic Discipline Project, and STCSM of China (No. 08ZR1408300, S30108, and 08DZ2231100)
文摘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.
文摘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.
基金supported by the National Basic Research Program of China(Grant No.2013CB733303)National Natural Science Foundation of China(Grant Nos.41274010,41371335)supported by PA-SB ESA EO Project Campaign of"Development of methods for Forest Biophysical Parameters Inversion Using POLIn SAR Data"(Grant No.ID.14655)
文摘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.
文摘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.