To reduce high computational cost of existing Direction-Of-Arrival(DOA) estimation techniques within a sparse representation framework,a novel method with low computational com-plexity is proposed.Firstly,a sparse lin...To reduce high computational cost of existing Direction-Of-Arrival(DOA) estimation techniques within a sparse representation framework,a novel method with low computational com-plexity is proposed.Firstly,a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built.Then based on the FOCal Underdetermined System Solver(FOCUSS) algorithm,a sparse solution finding algorithm to solve the model is developed.Compared with other state-of-the-art methods using a sparse representation,our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources.However,our method has lower computational complexity and performs better in low Signal-to-Noise Ratio(SNR).Lastly,the performance of the proposed method is illustrated by computer simulations.展开更多
Downward Looking Sparse Linear Array Three Dimensional SAR(DLSLA 3D SAR) is an important form of 3D SAR imaging, which has a widespread application field. Since its practical equivalent phase centers are usually distr...Downward Looking Sparse Linear Array Three Dimensional SAR(DLSLA 3D SAR) is an important form of 3D SAR imaging, which has a widespread application field. Since its practical equivalent phase centers are usually distributed sparsely and nonuniformly, traditional 3D SAR algorithms suffer from low resolution and high sidelobes in cross-track dimension. To deal with this problem, this paper introduces a method based on back-projection and convex optimization to achieve 3D high accuracy imaging reconstruction. Compared with traditional SAR algorithms, the proposed method sufficiently utilizes the sparsity of the 3D SAR imaging scene and can achieve lower sidelobes and higher resolution in cross-track dimension. In the simulated experiments, the reconstructed results of both simple and complex imaging scene verify that the proposed method outperforms 3D back-projection algorithm and shows satisfying cross-track dimensional resolution and good robustness to noise.展开更多
The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or ve...The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or very large complicated structures, we must use the parallel algorithm with the aid of high-performance computers to solve complex problems. This paper introduces the implementation process having the parallel with sparse linear equations from the perspective of sparse linear equation group.展开更多
In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimizati...In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system.The existence and uniqueness of the solution for the linear system are also proved.Experimental results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.展开更多
This paper describes a method of calculating the Schur complement of a sparse positive definite matrix A. The main idea of this approach is to represent matrix A in the form of an elimination tree using a reordering a...This paper describes a method of calculating the Schur complement of a sparse positive definite matrix A. The main idea of this approach is to represent matrix A in the form of an elimination tree using a reordering algorithm like METIS and putting columns/rows for which the Schur complement is needed into the top node of the elimination tree. Any problem with a degenerate part of the initial matrix can be resolved with the help of iterative refinement. The proposed approach is close to the “multifrontal” one which was implemented by Ian Duff and others in 1980s. Schur complement computations described in this paper are available in Intel®Math Kernel Library (Intel®MKL). In this paper we present the algorithm for Schur complement computations, experiments that demonstrate a negligible increase in the number of elements in the factored matrix, and comparison with existing alternatives.展开更多
The paper describes an efficient direct method to solve an equation Ax = b, where A is a sparse matrix, on the Intel®Xeon PhiTM coprocessor. The main challenge for such a system is how to engage all available ...The paper describes an efficient direct method to solve an equation Ax = b, where A is a sparse matrix, on the Intel®Xeon PhiTM coprocessor. The main challenge for such a system is how to engage all available threads (about 240) and how to reduce OpenMP* synchronization overhead, which is very expensive for hundreds of threads. The method consists of decomposing A into a product of lower-triangular, diagonal, and upper triangular matrices followed by solves of the resulting three subsystems. The main idea is based on the hybrid parallel algorithm used in the Intel®Math Kernel Library Parallel Direct Sparse Solver for Clusters [1]. Our implementation exploits a static scheduling algorithm during the factorization step to reduce OpenMP synchronization overhead. To effectively engage all available threads, a three-level approach of parallelization is used. Furthermore, we demonstrate that our implementation can perform up to 100 times better on factorization step and up to 65 times better in terms of overall performance on the 240 threads of the Intel®Xeon PhiTM coprocessor.展开更多
The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to th...The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is challenging.To address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve subsystems.Despite its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of subsystems.Furthermore,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear systems.To address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as αSetup-PCTL.The adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear systems.The proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall efficiency.Numerical results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.展开更多
The performance of linear prediction analysis of speech deteriorates rapidly under noisy environments. To tackle this issue, an improved noise-robust sparse linear prediction algorithm is proposed. First, the linear p...The performance of linear prediction analysis of speech deteriorates rapidly under noisy environments. To tackle this issue, an improved noise-robust sparse linear prediction algorithm is proposed. First, the linear prediction residual of speech is modeled as Student-t distribution, and the additive noise is incorporated explicitly to increase the robustness, thus a probabilistic model for sparse linear prediction of speech is built, Furthermore, variational Bayesian inference is utilized to approximate the intractable posterior distributions of the model parameters, and then the optimal linear prediction parameters are estimated robustly. The experimental results demonstrate the advantage of the developed algorithm in terms of several different metrics compared with the traditional algorithm and the l1 norm minimization based sparse linear prediction algorithm proposed in recent years. Finally it draws to a conclusion that the proposed algorithm is more robust to noise and is able to increase the speech quality in applications.展开更多
In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yi...In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yield a fast and efficient algorithm. Our alternating coordinate algorithm makes use of the sparsity of the coefficient matrix and the current residuals of the equations. Some hybrid techniques such as random restarts and genetic crossovers are also applied to improve our algorithm.展开更多
This paper focuses on error density estimation in ultrahigh dimensional sparse linear model,where the error term may have a heavy-tailed distribution.First,an improved two-stage refitted crossvalidation method combine...This paper focuses on error density estimation in ultrahigh dimensional sparse linear model,where the error term may have a heavy-tailed distribution.First,an improved two-stage refitted crossvalidation method combined with some robust variable screening procedures such as RRCS and variable selection methods such as LAD-SCAD is used to obtain the submodel,and then the residual-based kernel density method is applied to estimate the error density through LAD regression.Under given conditions,the large sample properties of the estimator are also established.Especially,we explicitly give the relationship between the sparsity and the convergence rate of the kernel density estimator.The simulation results show that the proposed error density estimator has a good performance.A real data example is presented to illustrate our methods.展开更多
Recent experience has shown that interior-point methods using a log barrierapproach are far superior to classical simplex methods for computing solutions to large parametricquantile regression problems. In many large ...Recent experience has shown that interior-point methods using a log barrierapproach are far superior to classical simplex methods for computing solutions to large parametricquantile regression problems. In many large empirical applications, the design matrix has a verysparse structure. A typical example is the classical fixed-effect model for panel data where theparametric dimension of the model can be quite large, but the number of non-zero elements is quitesmall. Adopting recent developments in sparse linear algebra we introduce a modified version of theFrisch-Newton algorithm for quantile regression described in Portnoy and Koenker[28]. The newalgorithm substantially reduces the storage (memory) requirements and increases computational speed.The modified algorithm also facilitates the development of nonparametric quantile regressionmethods. The pseudo design matrices employed in nonparametric quantile regression smoothing areinherently sparse in both the fidelity and roughness penalty components. Exploiting the sparsestructure of these problems opens up a whole range of new possibilities for multivariate smoothingon large data sets via ANOVA-type decomposition and partial linear models.展开更多
This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems.The method proposed is a generalization of the“operator expansion method”developed by Recchi...This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems.The method proposed is a generalization of the“operator expansion method”developed by Recchioni and Zirilli[SIAM J.Sci.Comput.,25(2003),1158-1186].The numerical method proposed reduces,via a perturbative approach,the solution of the scattering problem to the solution of a sequence of systems of first kind integral equations.The numerical solution of these systems of integral equations is challenging when scattering problems involving realistic obstacles and small wavelengths are solved.A computational method has been developed to solve these challenging problems with affordable computing resources.To this aim a new way of using the wavelet transform and new bases of wavelets are introduced,and a version of the operator expansion method is developed that constructs directly element by element in a fully parallelizable way.Several numerical experiments involving realistic obstacles and“small”wavelengths are proposed and high dimensional vector spaces are used in the numerical experiments.To evaluate the performance of the proposed algorithm on parallel computing facilities,appropriate speed up factors are introduced and evaluated.展开更多
基金Supported by the National Natural Science Foundation of China (No. 60502040)the Innovation Foundation for Outstanding Postgraduates in the Electronic Engineering Institute of PLA (No. 2009YB005)
文摘To reduce high computational cost of existing Direction-Of-Arrival(DOA) estimation techniques within a sparse representation framework,a novel method with low computational com-plexity is proposed.Firstly,a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built.Then based on the FOCal Underdetermined System Solver(FOCUSS) algorithm,a sparse solution finding algorithm to solve the model is developed.Compared with other state-of-the-art methods using a sparse representation,our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources.However,our method has lower computational complexity and performs better in low Signal-to-Noise Ratio(SNR).Lastly,the performance of the proposed method is illustrated by computer simulations.
基金Supported by the National Natural Science Foundation of China General Programs(Nos.61072112,61372186)the National Natural Science Foundation of China Key Program(No.60890071)
文摘Downward Looking Sparse Linear Array Three Dimensional SAR(DLSLA 3D SAR) is an important form of 3D SAR imaging, which has a widespread application field. Since its practical equivalent phase centers are usually distributed sparsely and nonuniformly, traditional 3D SAR algorithms suffer from low resolution and high sidelobes in cross-track dimension. To deal with this problem, this paper introduces a method based on back-projection and convex optimization to achieve 3D high accuracy imaging reconstruction. Compared with traditional SAR algorithms, the proposed method sufficiently utilizes the sparsity of the 3D SAR imaging scene and can achieve lower sidelobes and higher resolution in cross-track dimension. In the simulated experiments, the reconstructed results of both simple and complex imaging scene verify that the proposed method outperforms 3D back-projection algorithm and shows satisfying cross-track dimensional resolution and good robustness to noise.
文摘The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or very large complicated structures, we must use the parallel algorithm with the aid of high-performance computers to solve complex problems. This paper introduces the implementation process having the parallel with sparse linear equations from the perspective of sparse linear equation group.
基金Thanks for the reviewers’comments to improve the paper.This research was supported by the National Nature Science Foundation of China under Grant Nos.61772163,61761136010,61472111,Zhejiang Provincial Natural Science Foundation of China under Grant Nos.LR16F020003,LQ16F020005.
文摘In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system.The existence and uniqueness of the solution for the linear system are also proved.Experimental results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.
文摘This paper describes a method of calculating the Schur complement of a sparse positive definite matrix A. The main idea of this approach is to represent matrix A in the form of an elimination tree using a reordering algorithm like METIS and putting columns/rows for which the Schur complement is needed into the top node of the elimination tree. Any problem with a degenerate part of the initial matrix can be resolved with the help of iterative refinement. The proposed approach is close to the “multifrontal” one which was implemented by Ian Duff and others in 1980s. Schur complement computations described in this paper are available in Intel®Math Kernel Library (Intel®MKL). In this paper we present the algorithm for Schur complement computations, experiments that demonstrate a negligible increase in the number of elements in the factored matrix, and comparison with existing alternatives.
文摘The paper describes an efficient direct method to solve an equation Ax = b, where A is a sparse matrix, on the Intel®Xeon PhiTM coprocessor. The main challenge for such a system is how to engage all available threads (about 240) and how to reduce OpenMP* synchronization overhead, which is very expensive for hundreds of threads. The method consists of decomposing A into a product of lower-triangular, diagonal, and upper triangular matrices followed by solves of the resulting three subsystems. The main idea is based on the hybrid parallel algorithm used in the Intel®Math Kernel Library Parallel Direct Sparse Solver for Clusters [1]. Our implementation exploits a static scheduling algorithm during the factorization step to reduce OpenMP synchronization overhead. To effectively engage all available threads, a three-level approach of parallelization is used. Furthermore, we demonstrate that our implementation can perform up to 100 times better on factorization step and up to 65 times better in terms of overall performance on the 240 threads of the Intel®Xeon PhiTM coprocessor.
基金financially supported by the National Natural Science Foundation of China(62032023 and 11971414)Hunan National Applied Mathematics Center(2020ZYT003)the Research Foundation of Education Bureau of Hunan(21B0162).
文摘The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)problem.However,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is challenging.To address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve subsystems.Despite its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of subsystems.Furthermore,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear systems.To address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as αSetup-PCTL.The adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear systems.The proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall efficiency.Numerical results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.
基金supported by the Natural Science Foundation of Jiangsu Province(BK2012510,BK20140074)the National Postdoctoral Foundation of China(20090461424)
文摘The performance of linear prediction analysis of speech deteriorates rapidly under noisy environments. To tackle this issue, an improved noise-robust sparse linear prediction algorithm is proposed. First, the linear prediction residual of speech is modeled as Student-t distribution, and the additive noise is incorporated explicitly to increase the robustness, thus a probabilistic model for sparse linear prediction of speech is built, Furthermore, variational Bayesian inference is utilized to approximate the intractable posterior distributions of the model parameters, and then the optimal linear prediction parameters are estimated robustly. The experimental results demonstrate the advantage of the developed algorithm in terms of several different metrics compared with the traditional algorithm and the l1 norm minimization based sparse linear prediction algorithm proposed in recent years. Finally it draws to a conclusion that the proposed algorithm is more robust to noise and is able to increase the speech quality in applications.
文摘In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yield a fast and efficient algorithm. Our alternating coordinate algorithm makes use of the sparsity of the coefficient matrix and the current residuals of the equations. Some hybrid techniques such as random restarts and genetic crossovers are also applied to improve our algorithm.
基金Supported by the National Natural Science Foundation of China(Grant No.11971324)the State Key Program of National Natural Science Foundation of China(Grant No.12031016)。
文摘This paper focuses on error density estimation in ultrahigh dimensional sparse linear model,where the error term may have a heavy-tailed distribution.First,an improved two-stage refitted crossvalidation method combined with some robust variable screening procedures such as RRCS and variable selection methods such as LAD-SCAD is used to obtain the submodel,and then the residual-based kernel density method is applied to estimate the error density through LAD regression.Under given conditions,the large sample properties of the estimator are also established.Especially,we explicitly give the relationship between the sparsity and the convergence rate of the kernel density estimator.The simulation results show that the proposed error density estimator has a good performance.A real data example is presented to illustrate our methods.
基金This research was partially supported by NSF grant SES-02-40781.
文摘Recent experience has shown that interior-point methods using a log barrierapproach are far superior to classical simplex methods for computing solutions to large parametricquantile regression problems. In many large empirical applications, the design matrix has a verysparse structure. A typical example is the classical fixed-effect model for panel data where theparametric dimension of the model can be quite large, but the number of non-zero elements is quitesmall. Adopting recent developments in sparse linear algebra we introduce a modified version of theFrisch-Newton algorithm for quantile regression described in Portnoy and Koenker[28]. The newalgorithm substantially reduces the storage (memory) requirements and increases computational speed.The modified algorithm also facilitates the development of nonparametric quantile regressionmethods. The pseudo design matrices employed in nonparametric quantile regression smoothing areinherently sparse in both the fidelity and roughness penalty components. Exploiting the sparsestructure of these problems opens up a whole range of new possibilities for multivariate smoothingon large data sets via ANOVA-type decomposition and partial linear models.
文摘This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems.The method proposed is a generalization of the“operator expansion method”developed by Recchioni and Zirilli[SIAM J.Sci.Comput.,25(2003),1158-1186].The numerical method proposed reduces,via a perturbative approach,the solution of the scattering problem to the solution of a sequence of systems of first kind integral equations.The numerical solution of these systems of integral equations is challenging when scattering problems involving realistic obstacles and small wavelengths are solved.A computational method has been developed to solve these challenging problems with affordable computing resources.To this aim a new way of using the wavelet transform and new bases of wavelets are introduced,and a version of the operator expansion method is developed that constructs directly element by element in a fully parallelizable way.Several numerical experiments involving realistic obstacles and“small”wavelengths are proposed and high dimensional vector spaces are used in the numerical experiments.To evaluate the performance of the proposed algorithm on parallel computing facilities,appropriate speed up factors are introduced and evaluated.
