首页 > 最新文献

Applications of Mathematics最新文献

英文 中文
Maxwell-Schrödinger equations in singular electromagnetic field 奇异电磁场中的麦克斯韦-薛定谔方程
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-05-31 DOI: 10.21136/AM.2024.0180-23
Qihong Shi, Yaqian Jia, Jianwei Yang

We investigate the Cauchy problem of the one dimensional Maxwell-Schrödinger (MS) system under the Lorenz gauge condition. Different from the classical case, we consider the electromagnetic and electrostatic potentials which are growing at space infinity. More precisely, the electrostatic potential is allowed to grow linearly, while for the electromagnetic potential the growth is sublinear. Based on the energy estimates and the gauge transformation, we prove the global existence and the uniqueness of the weak solutions to this system.

我们研究了一维麦克斯韦-薛定谔(MS)系统在洛伦兹规条件下的考奇问题。与经典情况不同的是,我们考虑了在空间无穷大处增长的电磁势和静电势。更确切地说,静电势允许线性增长,而电磁势的增长是亚线性的。基于能量估计和量规变换,我们证明了该系统弱解的全局存在性和唯一性。
{"title":"Maxwell-Schrödinger equations in singular electromagnetic field","authors":"Qihong Shi,&nbsp;Yaqian Jia,&nbsp;Jianwei Yang","doi":"10.21136/AM.2024.0180-23","DOIUrl":"10.21136/AM.2024.0180-23","url":null,"abstract":"<div><p>We investigate the Cauchy problem of the one dimensional Maxwell-Schrödinger (MS) system under the Lorenz gauge condition. Different from the classical case, we consider the electromagnetic and electrostatic potentials which are growing at space infinity. More precisely, the electrostatic potential is allowed to grow linearly, while for the electromagnetic potential the growth is sublinear. Based on the energy estimates and the gauge transformation, we prove the global existence and the uniqueness of the weak solutions to this system.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 4","pages":"437 - 450"},"PeriodicalIF":0.6,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Energy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media 导电介质中稳定麦克斯韦方程的能量规范误差估计和收敛分析
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-05-27 DOI: 10.21136/AM.2024.0248-23
Eric Lindström, Larisa Beilina

The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell’s equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell’s equations also solves the wave equation, which makes computations very efficient. In this way our problem can be considered as a coupling problem, for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.

本文旨在研究导电介质中电场的时变麦克斯韦方程组在连续和离散环境下的拟合优度和解的稳定性,并研究采用的数值方案的收敛性分析。我们所考虑的情况代表一个物理问题,即在均质介质中出现一个子域,其特征是介电常数和电导函数恒定。众所周知,在这些均质区域中,麦克斯韦方程组的解同时也是波方程组的解,这使得计算非常高效。因此,我们的问题可视为一个耦合问题,并由此得出稳定性和收敛性分析。大量数值实例验证了所提出的稳定显式有限元方案的理论收敛率。
{"title":"Energy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media","authors":"Eric Lindström,&nbsp;Larisa Beilina","doi":"10.21136/AM.2024.0248-23","DOIUrl":"10.21136/AM.2024.0248-23","url":null,"abstract":"<div><p>The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell’s equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell’s equations also solves the wave equation, which makes computations very efficient. In this way our problem can be considered as a coupling problem, for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 4","pages":"415 - 436"},"PeriodicalIF":0.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2024.0248-23.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving inverse nodal problem with frozen argument by using second Chebyshev wavelet method 用第二切比雪夫小波法解决带冻结参数的反节点问题
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-04-17 DOI: 10.21136/AM.2024.0038-21
Yu Ping Wang, Shahrbanoo Akbarpoor Kiasary, Emrah Yılmaz

We consider the inverse nodal problem for Sturm-Liouville (S-L) equation with frozen argument. Asymptotic behaviours of eigenfunctions, nodal parameters are represented in two cases and numerical algorithms are produced to solve the given problems. Subsequently, solution of inverse nodal problem is calculated by the second Chebyshev wavelet method (SCW), accuracy and effectiveness of the method are shown in some numerical examples.

我们考虑了具有冻结参数的 Sturm-Liouville (S-L) 方程的反节点问题。特征函数的渐近行为、节点参数在两种情况下均有体现,并产生了解决给定问题的数值算法。随后,用第二切比雪夫小波方法(SCW)计算了反节点问题的解,并在一些数值示例中展示了该方法的准确性和有效性。
{"title":"Solving inverse nodal problem with frozen argument by using second Chebyshev wavelet method","authors":"Yu Ping Wang,&nbsp;Shahrbanoo Akbarpoor Kiasary,&nbsp;Emrah Yılmaz","doi":"10.21136/AM.2024.0038-21","DOIUrl":"10.21136/AM.2024.0038-21","url":null,"abstract":"<div><p>We consider the inverse nodal problem for Sturm-Liouville (S-L) equation with frozen argument. Asymptotic behaviours of eigenfunctions, nodal parameters are represented in two cases and numerical algorithms are produced to solve the given problems. Subsequently, solution of inverse nodal problem is calculated by the second Chebyshev wavelet method (SCW), accuracy and effectiveness of the method are shown in some numerical examples.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"339 - 354"},"PeriodicalIF":0.6,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140691512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula 基于特殊矩阵和乘积公式的对称 Sturm-Liouville 问题和反电势问题的特征值
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-04-08 DOI: 10.21136/AM.2024.0005-21
Chein-Shan Liu, Botong Li

The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in a linear space of trial functions by using the Gram-Schmidt orthonormalization technique. Then an n-dimensional matrix eigenvalue problem is derived with a special matrix A:= [aij], that is, aij = 0 if i + j is odd.

Based on the product formula, an integration method with a fictitious time, namely the fictitious time integration method (FTIM), is developed to obtain the higher-index eigenvalues. Also, we recover the symmetric potential function q(x) in the Sturm-Liouville operator by specifying a few lower-index eigenvalues, based on the product formula and the Newton iterative method.

如果系数是偶函数,边界条件是对称的,那么 Sturm-Liouville 特征值问题就是对称的。特征函数用正交基来表示,而正交基是通过格拉姆-施密特正交技术在试函数的线性空间中构建的。在乘积公式的基础上,发展出一种虚构时间的积分方法,即虚构时间积分法(FTIM),从而得到高指数特征值。此外,我们还根据乘积公式和牛顿迭代法,通过指定几个低指数特征值来恢复 Sturm-Liouville 算子中的对称势函数 q(x)。
{"title":"The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula","authors":"Chein-Shan Liu,&nbsp;Botong Li","doi":"10.21136/AM.2024.0005-21","DOIUrl":"10.21136/AM.2024.0005-21","url":null,"abstract":"<div><p>The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in a linear space of trial functions by using the Gram-Schmidt orthonormalization technique. Then an <i>n</i>-dimensional matrix eigenvalue problem is derived with a special matrix <b>A</b>:= [<i>a</i><sub><i>ij</i></sub>], that is, <i>a</i><sub><i>ij</i></sub> = 0 if <i>i</i> + <i>j</i> is odd.</p><p>Based on the product formula, an integration method with a fictitious time, namely the fictitious time integration method (FTIM), is developed to obtain the higher-index eigenvalues. Also, we recover the symmetric potential function <i>q</i>(<i>x</i>) in the Sturm-Liouville operator by specifying a few lower-index eigenvalues, based on the product formula and the Newton iterative method.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"355 - 372"},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations 求解复杂对称线性方程的双参数双步分裂迭代法
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-04-05 DOI: 10.21136/AM.2024.0133-23
Beibei Li, Jingjing Cui, Zhengge Huang, Xiaofeng Xie

We multiply both sides of the complex symmetric linear system Ax = b by 1 − iω to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.

我们将复对称线性系统 Ax = b 的两边乘以 1 - iω,得到一个新的等效线性系统,然后建立了一个双参数双步分裂(DDSS)方法来求解新的线性系统。此外,我们还提出了 DDSS 方法迭代矩阵谱半径的上界,并获得了其准最优参数。理论分析表明,当满足某些条件时,新方法是收敛的。我们还给出了一些测试实例来说明所提方法的有效性。
{"title":"A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations","authors":"Beibei Li,&nbsp;Jingjing Cui,&nbsp;Zhengge Huang,&nbsp;Xiaofeng Xie","doi":"10.21136/AM.2024.0133-23","DOIUrl":"10.21136/AM.2024.0133-23","url":null,"abstract":"<div><p>We multiply both sides of the complex symmetric linear system <i>Ax</i> = <i>b</i> by 1 − i<i>ω</i> to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"311 - 337"},"PeriodicalIF":0.6,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-point oscillatory solutions to system with relay hysteresis and nonperiodic external disturbance 具有中继滞后和非周期性外部干扰的系统的两点振荡解
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-04-02 DOI: 10.21136/AM.2024.0152-22
Alexander M. Kamachkin, Dmitriy K. Potapov, Victoria V. Yevstafyeva

We study an n-dimensional system of ordinary differential equations with a constant matrix, a relay-type nonlinearity, and an external disturbance in the right-hand side. We consider a nonideal relay characteristic. The external disturbance is described by the product of an exponential function and a sine function with an initial phase as a parameter. We assume the matrix of the linear part and the vector at the relay characteristic such that, by a nonsingular transformation, the system is reduced to the form with the diagonal matrix and the vector being opposite to the unit vector. We establish a necessary and sufficient condition for the existence of two-point oscillatory solutions, i.e., the solutions with two fixed points on the hyperplanes of the relay switching in phase space. Also, we give the sufficient conditions under which such solutions do not exist. We provide a supporting example, which demonstrates how to apply the obtained results.

我们研究了一个 n 维常微分方程系统,其右边包含一个常数矩阵、一个继电器型非线性和一个外部扰动。我们考虑了非理想继电器特性。外部扰动由指数函数和正弦函数的乘积描述,初始相位为参数。我们假设线性部分的矩阵和中继特性的矢量,通过非奇异变换,系统简化为对角矩阵和矢量与单位矢量相反的形式。我们建立了两点振荡解存在的必要条件和充分条件,即在相空间中继切换的超平面上有两个固定点的解。此外,我们还给出了此类解不存在的充分条件。我们提供了一个辅助示例,演示如何应用所获得的结果。
{"title":"Two-point oscillatory solutions to system with relay hysteresis and nonperiodic external disturbance","authors":"Alexander M. Kamachkin,&nbsp;Dmitriy K. Potapov,&nbsp;Victoria V. Yevstafyeva","doi":"10.21136/AM.2024.0152-22","DOIUrl":"10.21136/AM.2024.0152-22","url":null,"abstract":"<div><p>We study an <i>n</i>-dimensional system of ordinary differential equations with a constant matrix, a relay-type nonlinearity, and an external disturbance in the right-hand side. We consider a nonideal relay characteristic. The external disturbance is described by the product of an exponential function and a sine function with an initial phase as a parameter. We assume the matrix of the linear part and the vector at the relay characteristic such that, by a nonsingular transformation, the system is reduced to the form with the diagonal matrix and the vector being opposite to the unit vector. We establish a necessary and sufficient condition for the existence of two-point oscillatory solutions, i.e., the solutions with two fixed points on the hyperplanes of the relay switching in phase space. Also, we give the sufficient conditions under which such solutions do not exist. We provide a supporting example, which demonstrates how to apply the obtained results.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"395 - 414"},"PeriodicalIF":0.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media 解决非均质介质中二维准晶体的弹性力学问题
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-03-25 DOI: 10.21136/AM.2024.0045-23
Meltem Altunkaynak

Initial value problem for three dimensional (3D) elastodynamic system in two dimensional (2D) inhomogeneous quasicrystals is considered. An analytical method is studied for the solution of this problem. The system is written in terms of Fourier images of displacements with respect to lateral variables. The resulting problem is reduced to integral equations of the Volterra type. Finally, using Paley Wiener theorem it is shown that the solution of the initial value problem can be found by the inverse Fourier transform. A numerical example is considered for the comparison of the exact solution with the computed solution obtained by using the method.

考虑了二维(2D)不均匀准晶体中三维(3D)弹性动力系统的初值问题。研究了解决该问题的分析方法。该系统是用相对于横向变量的位移的傅立叶图像写成的。由此产生的问题被简化为 Volterra 型积分方程。最后,利用 Paley Wiener 定理证明,初值问题的解可以通过反傅里叶变换找到。通过一个数值示例,比较了精确解和使用该方法计算得出的解。
{"title":"Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media","authors":"Meltem Altunkaynak","doi":"10.21136/AM.2024.0045-23","DOIUrl":"10.21136/AM.2024.0045-23","url":null,"abstract":"<div><p>Initial value problem for three dimensional (3D) elastodynamic system in two dimensional (2D) inhomogeneous quasicrystals is considered. An analytical method is studied for the solution of this problem. The system is written in terms of Fourier images of displacements with respect to lateral variables. The resulting problem is reduced to integral equations of the Volterra type. Finally, using Paley Wiener theorem it is shown that the solution of the initial value problem can be found by the inverse Fourier transform. A numerical example is considered for the comparison of the exact solution with the computed solution obtained by using the method.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"289 - 309"},"PeriodicalIF":0.6,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140383945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On stochastic properties of past varentropy with applications 论过去透明性的随机特性及其应用
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-03-11 DOI: 10.21136/AM.2024.0163-23
Akash Sharma, Chanchal Kundu

To have accuracy in the extracted information is the goal of the reliability theory investigation. In information theory, varentropy has recently been proposed to describe and measure the degree of information dispersion around entropy. Theoretical investigation on varentropy of past life has been initiated, however details on its stochastic properties are yet to be discovered. In this paper, we propose a novel stochastic order and introduce new classes of life distributions based on past varentropy. Further, we illustrate some of its applications in reliability modeling and in the diversity measure of Boltzmann distribution.

精确提取信息是可靠性理论研究的目标。在信息论中,最近提出了熵来描述和测量信息在熵周围的分散程度。有关前世熵的理论研究已经开始,但有关其随机特性的细节仍有待发现。在本文中,我们提出了一种新的随机顺序,并基于过去熵引入了新的生命分布类别。此外,我们还说明了它在可靠性建模和波尔兹曼分布多样性度量中的一些应用。
{"title":"On stochastic properties of past varentropy with applications","authors":"Akash Sharma,&nbsp;Chanchal Kundu","doi":"10.21136/AM.2024.0163-23","DOIUrl":"10.21136/AM.2024.0163-23","url":null,"abstract":"<div><p>To have accuracy in the extracted information is the goal of the reliability theory investigation. In information theory, varentropy has recently been proposed to describe and measure the degree of information dispersion around entropy. Theoretical investigation on varentropy of past life has been initiated, however details on its stochastic properties are yet to be discovered. In this paper, we propose a novel stochastic order and introduce new classes of life distributions based on past varentropy. Further, we illustrate some of its applications in reliability modeling and in the diversity measure of Boltzmann distribution.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"373 - 394"},"PeriodicalIF":0.6,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Erratum to Fourier diffraction theorem for the tensor fields 张量场的傅立叶衍射定理的勘误
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-03-08 DOI: 10.21136/AM.2024.0056-24
Alexander Leonidovich Balandin
{"title":"Erratum to Fourier diffraction theorem for the tensor fields","authors":"Alexander Leonidovich Balandin","doi":"10.21136/AM.2024.0056-24","DOIUrl":"10.21136/AM.2024.0056-24","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"287 - 287"},"PeriodicalIF":0.6,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140077105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ridge estimation of covariance matrix from data in two classes 从两类数据中对协方差矩阵进行岭式估计
IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Pub Date : 2024-02-22 DOI: 10.21136/AM.2024.0157-23
Yi Zhou, Bin Zhang

This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether the data size is larger or smaller than the data dimension. Furthermore, the ridge parameter is tuned through a cross-validation procedure. Lastly, the proposed ridge estimator is verified with better performance than the existing estimator from the data in two classes and the traditional ridge estimator only from the good data.

摘要 本文论述了从两类数据中估计协方差矩阵的问题:(1) 具有相关协方差矩阵的良好数据;(2) 来自具有不同协方差矩阵的高斯分布的污染。为了解决从两类数据模型中估计协方差矩阵所面临的高维挑战,我们引入了脊惩罚。无论数据大小比数据维度大还是小,协方差矩阵的脊估计器都有统一的表达式,并保持正有限性。此外,脊参数还可以通过交叉验证程序进行调整。最后,验证了所提出的脊估计器在两类数据中的性能优于现有估计器,以及仅在良好数据中的传统脊估计器。
{"title":"Ridge estimation of covariance matrix from data in two classes","authors":"Yi Zhou,&nbsp;Bin Zhang","doi":"10.21136/AM.2024.0157-23","DOIUrl":"10.21136/AM.2024.0157-23","url":null,"abstract":"<div><p>This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether the data size is larger or smaller than the data dimension. Furthermore, the ridge parameter is tuned through a cross-validation procedure. Lastly, the proposed ridge estimator is verified with better performance than the existing estimator from the data in two classes and the traditional ridge estimator only from the good data.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"169 - 184"},"PeriodicalIF":0.6,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
期刊
Applications of Mathematics
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1