A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with...A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.展开更多
In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations i...In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented.展开更多
By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded s...By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szego projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szego kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.展开更多
With the progress and development of science, the synchronous satellite as the high-tech product is taken something more and more seriously by all countries. Converting gray value matrix into geographic coordinates be...With the progress and development of science, the synchronous satellite as the high-tech product is taken something more and more seriously by all countries. Converting gray value matrix into geographic coordinates becomes more and more important. This paper establishes the models for interconverting row and column of gray value matrix which detected by the infrared detectors on synchronous satellites and geographic coordinates based on the related theorems and properties of space analytic geometry. We draw satellite cloud image with the data of gray matrix in MATLAB, convert coastline’s latitude and longitude coordinates into row and column coordinates of a gray matrix according via these models when the sub-satellite point’s row and column coordinates and geographic coordinates are given, then add coast-lines to the original satellite cloud image with the transformation data. We find that coast-lines completely match with the bump characteristics of satellite cloud image, and that verify the correctness of the models.展开更多
Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a ...Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.展开更多
文摘A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.
基金Supported by the Youth Mainstay Teacher Foundation of HunanProvince Educational Committee
文摘In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented.
基金supported by Portuguese funds through the CIDMA Center for Research and Development in Mathematics and Applicationsthe Portuguese Foundation for Science and Technology(FCT–Fundao para a Ciência e a Tecnologia)within project UID/MAT/04106/2013the recipient of a Postdoctoral Foundation from FCT under Grant No. SFRH/BPD/74581/2010
文摘By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szego projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szego kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.
文摘With the progress and development of science, the synchronous satellite as the high-tech product is taken something more and more seriously by all countries. Converting gray value matrix into geographic coordinates becomes more and more important. This paper establishes the models for interconverting row and column of gray value matrix which detected by the infrared detectors on synchronous satellites and geographic coordinates based on the related theorems and properties of space analytic geometry. We draw satellite cloud image with the data of gray matrix in MATLAB, convert coastline’s latitude and longitude coordinates into row and column coordinates of a gray matrix according via these models when the sub-satellite point’s row and column coordinates and geographic coordinates are given, then add coast-lines to the original satellite cloud image with the transformation data. We find that coast-lines completely match with the bump characteristics of satellite cloud image, and that verify the correctness of the models.
基金The project supported by the National Natural Science Foundation of China(19672043)
文摘Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.
