By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general sol...By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general solution or unique solution.展开更多
A matrix A ∈ Mn（C） is called generalized normal provided that there is a positive definite Hermite matrix H such that HAH is normal. In this paper, these matrices are investigated and their canonical form, invarian...A matrix A ∈ Mn（C） is called generalized normal provided that there is a positive definite Hermite matrix H such that HAH is normal. In this paper, these matrices are investigated and their canonical form, invariants and relative properties in the sense of congruence are obtained.展开更多
In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized...In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.展开更多
This paper is concerned with the normalized Laplacian spectra of four variants of double join operations based on subdivision graph,Q-graph,R-graph and total graph.The results here generalize some well known results a...This paper is concerned with the normalized Laplacian spectra of four variants of double join operations based on subdivision graph,Q-graph,R-graph and total graph.The results here generalize some well known results about some join operations of graphs.展开更多
对深空网天线组阵中的几种信号相关算法作简要介绍,重点研究无需形成矩阵的幂的方法——Matrix-Free Power Method。通过理论分析,提出一种改进算法,即基于归一化权的Matrix-Free Power Method。理论计算和软件仿真结果均表明,基于归一...对深空网天线组阵中的几种信号相关算法作简要介绍,重点研究无需形成矩阵的幂的方法——Matrix-Free Power Method。通过理论分析,提出一种改进算法,即基于归一化权的Matrix-Free Power Method。理论计算和软件仿真结果均表明,基于归一化权的Matrix-Free Power Method信噪比合成性能略优于原Matrix-Free Power Method。展开更多
In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalize...In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.展开更多
Boundary Element Method (BEM) is widely used in electrocardiographic (ECG) problem. Formulations of these problems based on mathematical and numerical approximations of the known source in heart and the volume conduct...Boundary Element Method (BEM) is widely used in electrocardiographic (ECG) problem. Formulations of these problems based on mathematical and numerical approximations of the known source in heart and the volume conductor that can transfer voltages on the surface of the body. To analyze the electric potentials on body surface or epicardial surface, a set of discrete equations derived from a boundary integral equations need to be solved. Solving these equations means to get the potential distribution eventually. In the process of solving, transfer matrix of discrete equations has received considerable attention, how to get an appropriate transfer matrix is an important issue. This paper found that the direction of normal vector could affect the results when calculating the transfer matrix and presents a method analogous to Mesh Current Method to deal with this direction problem. Several simulations have been carried out to verify the accurate results with the correct direction of normal vector using new method within a torso model given simultaneous epicardial and body surface potential recordings.展开更多
Starting from the wave normal tracing treatment in the Savart polariscope that relates the Jones matrix to its transmission performance, this paper establishes a simple and effective model for the Jones matrix at an a...Starting from the wave normal tracing treatment in the Savart polariscope that relates the Jones matrix to its transmission performance, this paper establishes a simple and effective model for the Jones matrix at an arbitrary incidence in the spatial domain. Analytical expressions of all the matrix components are determined with the consideration of all the main impact factors. This model needs only a few parameters hence it is convenient to be employed to evaluate the propagation performance of any birefringent optical system. The simulated results obtained with it demonstrate that this model gives a precise representation of the characteristic of light propagation in the Savart polariscope. This would provide useful suggestions for the design, calibration, and performance improvement of any other birefringent polarisation element and optical system.展开更多
As one of the most essential and important operations in linear algebra, the performance prediction of sparse matrix-vector multiplication (SpMV) on GPUs has got more and more attention in recent years. In 2012, Guo a...As one of the most essential and important operations in linear algebra, the performance prediction of sparse matrix-vector multiplication (SpMV) on GPUs has got more and more attention in recent years. In 2012, Guo and Wang put forward a new idea to predict the performance of SpMV on GPUs. However, they didn’t consider the matrix structure completely, so the execution time predicted by their model tends to be inaccurate for general sparse matrix. To address this problem, we proposed two new similar models, which take into account the structure of the matrices and make the performance prediction model more accurate. In addition, we predict the execution time of SpMV for CSR-V, CSR-S, ELL and JAD sparse matrix storage formats by the new models on the CUDA platform. Our experimental results show that the accuracy of prediction by our models is 1.69 times better than Guo and Wang’s model on average for most general matrices.展开更多
In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become i...In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.展开更多
The main drawback of current ECG systems is the location-specific nature of the systems due to the use of fixed/wired applications. That is why there is a critical need to improve the current ECG systems to achieve ex...The main drawback of current ECG systems is the location-specific nature of the systems due to the use of fixed/wired applications. That is why there is a critical need to improve the current ECG systems to achieve extended patient’s mobility and to cover security handling. With this in mind, Compressed Sensing (CS) procedure and the collaboration of Sensing Matrix Selection (SMS) approach are used to provide a robust ultra-low-power approach for normal and abnormal ECG signals. Our simulation results based on two proposed algorithms illustrate 25% decrease in sampling-rate and a good level of quality for the degree of incoherence between the random measurement and sparsity matrices. The simulation results also confirm that the Binary Toeplitz Matrix (BTM) provides the best compression performance with the highest energy efficiency for random sensing matrix.展开更多
The global gravitational model can be expressed as a series of spherical harmonic coefficients computed up to a certain degree and order.The main ordering characteristic can depend on the degree,order,or type of coeff...The global gravitational model can be expressed as a series of spherical harmonic coefficients computed up to a certain degree and order.The main ordering characteristic can depend on the degree,order,or type of coefficient.When determining the spherical harmonic coefficients using the least squares method,it is essential to analyze the ordering pattern of these coefficients and their positions(e.g.,indices)in the vector or matrix.A systematic analysis on the type of coefficient arrangement is presented in this paper.Moreover,the index algorithm for each coefficient ordering pattern is provided.Additionally,the structure of the normal equation matrix with different coefficient arrangement patterns is analyzed.Based on the analysis and the algorithm presented in this paper:(1)we can calculate the index of each coefficient in the vector or matrix of the normal equation;(2)we can change the structure of the normal equation matrix of the Earth’s gravity field from one type of coefficient arrangement to another.Furthermore,(3)we can directly combine different structures of the normal equation matrix,calculated from different types of gravity satellite missions,to form combined normal equations.This approach is beneficial for the determination of Earth’s gravitational model using multi-type observation data.展开更多
基金the NSF of Hunan Province and the Science and Technology Development Foundation of Xiangtan Polytechnic University
文摘By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general solution or unique solution.
基金Natural Science Foundation of Jiangsu Province(BK2007030)the National Natural Science Foundation of China(10471037)the Natural Science Foundation of the Education Committee of Jiangsu Province(07KJD110207,06KJD110179).
文摘A matrix A ∈ Mn（C） is called generalized normal provided that there is a positive definite Hermite matrix H such that HAH is normal. In this paper, these matrices are investigated and their canonical form, invariants and relative properties in the sense of congruence are obtained.
文摘In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.
基金Supported by the National Natural Science Foundation of China(Grant No.11961040)the Natural Science Foundation of Gansu Province(Grant No.20JR5RA418)。
文摘This paper is concerned with the normalized Laplacian spectra of four variants of double join operations based on subdivision graph,Q-graph,R-graph and total graph.The results here generalize some well known results about some join operations of graphs.
文摘对深空网天线组阵中的几种信号相关算法作简要介绍,重点研究无需形成矩阵的幂的方法——Matrix-Free Power Method。通过理论分析,提出一种改进算法,即基于归一化权的Matrix-Free Power Method。理论计算和软件仿真结果均表明,基于归一化权的Matrix-Free Power Method信噪比合成性能略优于原Matrix-Free Power Method。
基金This work was supported by National Natural Science Foundation of China(No.60710002)Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT).
文摘In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.
文摘Boundary Element Method (BEM) is widely used in electrocardiographic (ECG) problem. Formulations of these problems based on mathematical and numerical approximations of the known source in heart and the volume conductor that can transfer voltages on the surface of the body. To analyze the electric potentials on body surface or epicardial surface, a set of discrete equations derived from a boundary integral equations need to be solved. Solving these equations means to get the potential distribution eventually. In the process of solving, transfer matrix of discrete equations has received considerable attention, how to get an appropriate transfer matrix is an important issue. This paper found that the direction of normal vector could affect the results when calculating the transfer matrix and presents a method analogous to Mesh Current Method to deal with this direction problem. Several simulations have been carried out to verify the accurate results with the correct direction of normal vector using new method within a torso model given simultaneous epicardial and body surface potential recordings.
基金Project supported by the State Key Program of National Natural Science Foundation of China (Grant No. 40537031)the National Natural Science Foundation of China (Grant No. 40875013)+1 种基金the National Defense Basic Scientific Research Project,China (Grant No. A1420080187)the National High Technology Research and Development Program of China (Grant No. 2006AA12Z152)
文摘Starting from the wave normal tracing treatment in the Savart polariscope that relates the Jones matrix to its transmission performance, this paper establishes a simple and effective model for the Jones matrix at an arbitrary incidence in the spatial domain. Analytical expressions of all the matrix components are determined with the consideration of all the main impact factors. This model needs only a few parameters hence it is convenient to be employed to evaluate the propagation performance of any birefringent optical system. The simulated results obtained with it demonstrate that this model gives a precise representation of the characteristic of light propagation in the Savart polariscope. This would provide useful suggestions for the design, calibration, and performance improvement of any other birefringent polarisation element and optical system.
文摘As one of the most essential and important operations in linear algebra, the performance prediction of sparse matrix-vector multiplication (SpMV) on GPUs has got more and more attention in recent years. In 2012, Guo and Wang put forward a new idea to predict the performance of SpMV on GPUs. However, they didn’t consider the matrix structure completely, so the execution time predicted by their model tends to be inaccurate for general sparse matrix. To address this problem, we proposed two new similar models, which take into account the structure of the matrices and make the performance prediction model more accurate. In addition, we predict the execution time of SpMV for CSR-V, CSR-S, ELL and JAD sparse matrix storage formats by the new models on the CUDA platform. Our experimental results show that the accuracy of prediction by our models is 1.69 times better than Guo and Wang’s model on average for most general matrices.
文摘In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.
文摘The main drawback of current ECG systems is the location-specific nature of the systems due to the use of fixed/wired applications. That is why there is a critical need to improve the current ECG systems to achieve extended patient’s mobility and to cover security handling. With this in mind, Compressed Sensing (CS) procedure and the collaboration of Sensing Matrix Selection (SMS) approach are used to provide a robust ultra-low-power approach for normal and abnormal ECG signals. Our simulation results based on two proposed algorithms illustrate 25% decrease in sampling-rate and a good level of quality for the degree of incoherence between the random measurement and sparsity matrices. The simulation results also confirm that the Binary Toeplitz Matrix (BTM) provides the best compression performance with the highest energy efficiency for random sensing matrix.
基金supported by The National Natural Science Foundation of China(42374004).
文摘The global gravitational model can be expressed as a series of spherical harmonic coefficients computed up to a certain degree and order.The main ordering characteristic can depend on the degree,order,or type of coefficient.When determining the spherical harmonic coefficients using the least squares method,it is essential to analyze the ordering pattern of these coefficients and their positions(e.g.,indices)in the vector or matrix.A systematic analysis on the type of coefficient arrangement is presented in this paper.Moreover,the index algorithm for each coefficient ordering pattern is provided.Additionally,the structure of the normal equation matrix with different coefficient arrangement patterns is analyzed.Based on the analysis and the algorithm presented in this paper:(1)we can calculate the index of each coefficient in the vector or matrix of the normal equation;(2)we can change the structure of the normal equation matrix of the Earth’s gravity field from one type of coefficient arrangement to another.Furthermore,(3)we can directly combine different structures of the normal equation matrix,calculated from different types of gravity satellite missions,to form combined normal equations.This approach is beneficial for the determination of Earth’s gravitational model using multi-type observation data.
