The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of ...The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of symmetric tridiagonal matrix. The multisection method for solving the generalized eigenproblem applied significantly in many science and engineering domains has not been studied. The parallel region preserving multisection method (PRM for short) for solving generalized eigenproblems of large sparse and real symmetric matrix is presented in this paper. This method not only retains the advantages of the conventional determinant search method (DS for short), but also overcomes its disadvantages such as leaking roots and disconvergence. We have tested the method on the YH 1 vector computer, and compared it with the parallel region preserving determinant search method the parallel region preserving bisection method (PRB for short). The numerical results show that PRM has a higher speed up, for instance, it attains the speed up of 7.7 when the scale of the problem is 2 114 and the eigenpair found is 3, and PRM is superior to PRB when the scale of the problem is large.展开更多
In(relativistic)electronic structure methods,the quaternion matrix eigenvalue problem and the linear response(Bethe-Salpeter)eigenvalue problem for excitation energies are two frequently encoun-tered structured eigenv...In(relativistic)electronic structure methods,the quaternion matrix eigenvalue problem and the linear response(Bethe-Salpeter)eigenvalue problem for excitation energies are two frequently encoun-tered structured eigenvalue problems.While the former problem was thoroughly studied,the later problem in its most general form,namely,the complex case without assuming the positive definiteness of the electronic Hessian,was not fully understood.In view of their very similar mathematical structures,we examined these two problems from a unified point of view.We showed that the identification of Lie group structures for their eigenvectors provides a framework to design diagonalization algorithms as well as numerical optimizations techniques on the corresponding manifolds.By using the same reduction algorithm for the quaternion matrix eigenvalue problem,we provided a necessary and sufficient condition to characterize the different scenarios,where the eigenvalues of the original linear response eigenvalue problem are real,purely imaginary,or complex.The result can be viewed as a natural generalization of the well-known condition for the real matrix case.展开更多
We present a differential geometric perspective of the IEP for symmetric matrices in the framework of a fibre bundle with structure group SO（n）. In particular, a Newton type algorithm is developed to construct a non...We present a differential geometric perspective of the IEP for symmetric matrices in the framework of a fibre bundle with structure group SO（n）. In particular, a Newton type algorithm is developed to construct a non singular symmetric matrix for given target eigenvalues using a singular symmetric matrix as the initial matrix for the iteration. Explicit computations are performed for 2 x 2 non singular symmetric matrix to illustrate the result.展开更多
This paper presented an individual recognition algorithm for human iris using fractal dimension of grayscale extremums for feature extraction.Firstly,iris region was localized from an eye image with modified circle de...This paper presented an individual recognition algorithm for human iris using fractal dimension of grayscale extremums for feature extraction.Firstly,iris region was localized from an eye image with modified circle detector stemmed from Daugman’s integro-differential operator.Then,segmentation was used to extract the iris and to exclude occlusion from eyelids and eyelashes.The extracted iris was normalized and mapped to polar coordinates for matching.In feature encoding,a new approach based on fractal dimension of grayscale extremums was designed to extract textural features of iris.Finally,a normalized correlation classifier was employed to determine the agreement of two iris feature templates,and the feature template was rotated left and right to avoid the interference from rotation of eyes and tilting of head.The experimental results show that fractal dimension of grayscale extremums can extract textural features from iris image effectively,and the proposed recognition algorithm is accurate and efficient.The proposed algorithm was tested on CASIA-IrisV3-Interval iris database and the performance was evaluated based on the analysis of both False Accept Rate(FAR)and False Reject Rate(FRR)curves.Experimental results show that the proposed iris recognition algorithm is effective and efficient.展开更多
Due to the presence of graphite flake cascades, the real graphite anode of Li-ion battery shows non-iso- tropic characteristic. The present work developed an ellipsoid-based simulated annealing method and numeri- call...Due to the presence of graphite flake cascades, the real graphite anode of Li-ion battery shows non-iso- tropic characteristic. The present work developed an ellipsoid-based simulated annealing method and numeri- cally reconstructed the three-dimensional microstructure of a graphite anode. The reconstructed anode is a composite of three clearly distinguished phases： pore （or electrolyte）, graphite, and solid additives, well representing the non- isotropic heterogeneous characteristic of real graphite anode. Characterization analysis of the reconstructed electrode gives information such as the connectivity of individual phase, the specific interracial area between solid and pore phase, and the pore size distribution. The effects of the ellipsoid size on the structural characteristics of graphite anode were particularly studied. As the size of the ellipsoidal particle slightly increases, the average pore diameter increases and as a result the specific interfacial area between the solid and pore phase in the reconstructed area decreases; compared with the equatorial radius, the polar radius of ellipsoidal graphite particles has more sig- nificant influence on the characteristics of electrode microstructure.展开更多
This paper constructs a new spectrum of networks by means of the matrix of link-state ofthe network,which can reveal the characteristics of the correlation between the degrees of the network.Also,the computation of th...This paper constructs a new spectrum of networks by means of the matrix of link-state ofthe network,which can reveal the characteristics of the correlation between the degrees of the network.Also,the computation of this spectrum of networks is usually more feasible and more efficient due tothe much lower order of its matrix of link-state than its adjacent matrix in practice.Some estimatesfor the bounds of the key eigenvalues in the spectrum are obtained,the corresponding inequalities arepresented and proved.For the sake of its application,the authors define spectrum of networks in twoways,and all theorems are given in parallel for both kinds of definition.In addition,the authors finda symmetry in the spectrum,which is relative to the characteristic of structure of its network to someextent.展开更多
文摘The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of symmetric tridiagonal matrix. The multisection method for solving the generalized eigenproblem applied significantly in many science and engineering domains has not been studied. The parallel region preserving multisection method (PRM for short) for solving generalized eigenproblems of large sparse and real symmetric matrix is presented in this paper. This method not only retains the advantages of the conventional determinant search method (DS for short), but also overcomes its disadvantages such as leaking roots and disconvergence. We have tested the method on the YH 1 vector computer, and compared it with the parallel region preserving determinant search method the parallel region preserving bisection method (PRB for short). The numerical results show that PRM has a higher speed up, for instance, it attains the speed up of 7.7 when the scale of the problem is 2 114 and the eigenpair found is 3, and PRM is superior to PRB when the scale of the problem is large.
基金supported by the National Natural Science Foundation of China (No.21973003)the Beijing Normal University Startup Package
文摘In(relativistic)electronic structure methods,the quaternion matrix eigenvalue problem and the linear response(Bethe-Salpeter)eigenvalue problem for excitation energies are two frequently encoun-tered structured eigenvalue problems.While the former problem was thoroughly studied,the later problem in its most general form,namely,the complex case without assuming the positive definiteness of the electronic Hessian,was not fully understood.In view of their very similar mathematical structures,we examined these two problems from a unified point of view.We showed that the identification of Lie group structures for their eigenvectors provides a framework to design diagonalization algorithms as well as numerical optimizations techniques on the corresponding manifolds.By using the same reduction algorithm for the quaternion matrix eigenvalue problem,we provided a necessary and sufficient condition to characterize the different scenarios,where the eigenvalues of the original linear response eigenvalue problem are real,purely imaginary,or complex.The result can be viewed as a natural generalization of the well-known condition for the real matrix case.
文摘We present a differential geometric perspective of the IEP for symmetric matrices in the framework of a fibre bundle with structure group SO（n）. In particular, a Newton type algorithm is developed to construct a non singular symmetric matrix for given target eigenvalues using a singular symmetric matrix as the initial matrix for the iteration. Explicit computations are performed for 2 x 2 non singular symmetric matrix to illustrate the result.
基金supported by the Independent Innovation Foundation of Shandong University(No.2009JC004)the Program of Development of Science and Technology of Shandong(No.2010GSF10243)
文摘This paper presented an individual recognition algorithm for human iris using fractal dimension of grayscale extremums for feature extraction.Firstly,iris region was localized from an eye image with modified circle detector stemmed from Daugman’s integro-differential operator.Then,segmentation was used to extract the iris and to exclude occlusion from eyelids and eyelashes.The extracted iris was normalized and mapped to polar coordinates for matching.In feature encoding,a new approach based on fractal dimension of grayscale extremums was designed to extract textural features of iris.Finally,a normalized correlation classifier was employed to determine the agreement of two iris feature templates,and the feature template was rotated left and right to avoid the interference from rotation of eyes and tilting of head.The experimental results show that fractal dimension of grayscale extremums can extract textural features from iris image effectively,and the proposed recognition algorithm is accurate and efficient.The proposed algorithm was tested on CASIA-IrisV3-Interval iris database and the performance was evaluated based on the analysis of both False Accept Rate(FAR)and False Reject Rate(FRR)curves.Experimental results show that the proposed iris recognition algorithm is effective and efficient.
基金supported by the Key Scientific Development Project of Guangdong Province(2015A030308019)the Guangzhou Scientific and Technological Development Plan(2014J4100217)the Hundred Talents Program of Chinese Academy of Sciences
文摘Due to the presence of graphite flake cascades, the real graphite anode of Li-ion battery shows non-iso- tropic characteristic. The present work developed an ellipsoid-based simulated annealing method and numeri- cally reconstructed the three-dimensional microstructure of a graphite anode. The reconstructed anode is a composite of three clearly distinguished phases： pore （or electrolyte）, graphite, and solid additives, well representing the non- isotropic heterogeneous characteristic of real graphite anode. Characterization analysis of the reconstructed electrode gives information such as the connectivity of individual phase, the specific interracial area between solid and pore phase, and the pore size distribution. The effects of the ellipsoid size on the structural characteristics of graphite anode were particularly studied. As the size of the ellipsoidal particle slightly increases, the average pore diameter increases and as a result the specific interfacial area between the solid and pore phase in the reconstructed area decreases; compared with the equatorial radius, the polar radius of ellipsoidal graphite particles has more sig- nificant influence on the characteristics of electrode microstructure.
基金supported by the Key Project for Fundamental Research of STCSM under Grant No. 06JC14057
文摘This paper constructs a new spectrum of networks by means of the matrix of link-state ofthe network,which can reveal the characteristics of the correlation between the degrees of the network.Also,the computation of this spectrum of networks is usually more feasible and more efficient due tothe much lower order of its matrix of link-state than its adjacent matrix in practice.Some estimatesfor the bounds of the key eigenvalues in the spectrum are obtained,the corresponding inequalities arepresented and proved.For the sake of its application,the authors define spectrum of networks in twoways,and all theorems are given in parallel for both kinds of definition.In addition,the authors finda symmetry in the spectrum,which is relative to the characteristic of structure of its network to someextent.
