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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...
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....
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...
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...
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...
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.
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...
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...
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...
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...
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...
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...
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...
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...

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