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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals
光子晶体 线性非线性特征值问题 近似 计算
2023/5/15
In this talk, we discuss the approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals. We discretize the shifted Maxwell operator with edge finite elements a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some estimates on an exterior Steklov eigenvalue problem
外部 斯特克洛夫特征值 估计
2023/5/9
In this talk we will discuss a Steklov eigenvalue problem on an exterior Euclidean domain. We will present sharp lower and upper bounds for its first eigenvalue under various conditions on the domain....
2017年特征值问题的理论，计算和应用研讨会（Eigenvalue Problems:Theory,Approximation and Applications）
2017年 特征值问题的理论，计算和应用 研讨会
2017/11/24
Eigenvalue problems arise in many scientific and engineering applications. They are also important in emerging areas such as big data analysis. For example, eigenvalues (or singular values) can be use...
三亚国际数学论坛：Eigenvalue Problems:Theory,Approximation,and Applications
三亚国际数学论坛 Eigenvalue Problems Theory Approximation Applications
2017/7/3
Eigenvalue problems arise in many scientific and engineering applications. They are also important in emerging areas such as big data analysis. For example, eigenvalues (or singular values) can be use...
ON THE DISTRIBUTION OF THE LARGEST EIGENVALUE IN PRINCIPAL COMPONENTS ANALYSIS
LARGEST EIGENVALUE PRINCIPAL COMPONENTS
2015/8/20
Let x1 denote the square of the largest singular value of an n × p
matrix X, all of whose entries are independent standard Gaussian varates. Equivalently, x1 is the largest principal component vari...
Solving interpolation problems via generalized eigenvalue minimization
Generalized eigenvalue interpolation control system the analysis of linear matrix inequality
2015/8/12
A number of problems in the analysis and design of control systems may be reformulated as the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices which depend affi...
Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem
Sturm-Liouville eigenvalue applications n-body problem
2015/3/18
Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem.
Accelerated solution of the frequency-domain Maxwell’s equations by engineering the eigenvalue distribution of the operator
Numerical approximation analysis Mathematical methods physics Mathematics
2015/8/7
We introduce a simple method to accelerate the convergence of iterative solvers of the frequency-domain Maxwell’s equations for deep-subwavelength structures. Using the continuity equation, the method...
Designing Optical Fibers: Fitting the Derivatives of a Nonlinear Pde-Eigenvalue Problem
Symmetric Indefinite Eigenvalue Gradient Optical Fiber Design
2013/1/30
When trying to fit data to functions of the eigensystem of a pde-eigenvalue problem, such as Maxwell’s equation, numerical differentiation is ineffective and analytic gradients must be supplied. In ou...
A Type of Multigrid Method for Eigenvalue Problem
Eigenvalue problem multigrid multi-level correction finiteelement method
2012/8/10
In this paper, a new type of iteration method is proposed to solve eigenvalue
problem by finite element method. With this new scheme, solving
eigenvalue problem is transformed to solving a series of...
Numerical Approximations of A Nonlinear Eigenvalue Problem and Applications to A Density Functional Model
Eigenvalue Galerkin discretization nonlinear numerical approximation density func- tional orbital-free
2012/8/10
In this paper, we study numerical approximations of a nonlinear eigenvalue problem and consider
applications to a density functional model. We prove the convergence of numerical approximations.
In p...
A Local Computational Scheme for Higher Order Finite Element Eigenvalue Approximations
Eigenvalue 痭 ite element higher order local computation
2012/8/8
Based on some coupled discretizations, a local computational scheme is proposed
and analyzed in this paper for a class of higher order 痭ite element eigenvalue approximations. Its
e眂iency is proven b...
One Approach to Construction of Bilateral Approximations Methods for Solution of Nonlinear Eigenvalue Problems
Nonlinear Eigenvalue Problem Derivatives of Matrix Determinant Numerical Algorithm of Alternate Approximations
2013/1/30
In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the conv...
Local Eigenvalue Density for General MANOVA Matrices
MANOVA random matrix Jacobi ensemble Local density of eigenvalues
2012/7/9
We consider random $n\times n$ matrices of the form $(XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2}$, where $X$ and $Y$ have independent entries with zero mean and variance one. These matrices are the natural ge...
Eigenvalue distributions from a star product approach
Eigenvalue distributions star product approach Mathematical Physics
2012/6/21
We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimensio...