相关论文: On the shift-invert Lanczos method for the bucklin…

This paper studies eigenvalues of the buckling problem of arbitrary order on bounded domains in Euclidean spaces and spheres. We prove universal bounds for the k-th eigenvalue in terms of the lower ones independent of the domains. Our…

This article focuses on solving the generalized eigenvalue problems (GEP) arising in the source-free Maxwell equation with magnetoelectric coupling effects that models three-dimensional complex media. The goal is to compute the smallest…

This work considers large-scale Lyapunov matrix equations of the form $AX + XA = \boldsymbol{c}\boldsymbol{c}^T$, where $A$ is a symmetric positive definite matrix and $\boldsymbol{c}$ is a vector. Motivated by the need to solve such…

We present a randomized, inverse-free algorithm for producing an approximate diagonalization of any $n \times n$ matrix pencil $(A,B)$. The bulk of the algorithm rests on a randomized divide-and-conquer eigensolver for the generalized…

Reliable adaptive beamforming is critical for large microphone arrays operating in highly dynamic acoustic environments. In scenarios characterized by fast-moving talkers and interferers, the available sample support for estimating the…

We consider an inverse spectral problem for a class of singular AKNS operators $H\_a, a\in\N$ with an explicit singularity. We construct for each $a\in\N$, a standard map $\lambda^a\times\kappa^a$ with spectral data $\lambda^a$ and some…

A deflated and restarted Lanczos algorithm to solve hermitian linear systems, and at the same time compute eigenvalues and eigenvectors for application to multiple right-hand sides, is described. For the first right-hand side, eigenvectors…

We study the Cauchy problem for the equation of the form $$ \ddot{u}(t) + (\aa A + B)\dot{u}(t) + (A+G)u(t) = 0,\tag* $$ where $A$, $B$, and $G$ are \o s in a Hilbert space $\Cal H$ with $A$ selfadjoint, $\sigma(A)=[0,\infty)$, $B\ge0$…

In this paper we consider the free-form optimization of eigenvalues in electromagnetic systems by means of shape-variations with respect to small deformations. The objective is to optimize a particular eigenvalue to a target value. We…

We establish that the spin-3/2 AKLT model on the honeycomb has a nonzero spectral gap. We use the relation between the anticommutator of two projectors and their sum, and apply it to related AKLT projectors that occupy plaquettes or other…

Quadratic forms of Hermitian matrix resolvents involve the solutions of shifted linear systems. Efficient iterative solutions use the shift-invariance property of Krylov subspaces The Hermitian Lanczos method reduces a given vector and…

We prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \epsilon I_{\mathcal{H}}$ for some $\epsilon…

We consider one-dimensional inverse scattering in attenuating media where both the reflectivity and loss distributions are unknown. Mathematically, this corresponds to recovering the coefficients of a damped wave operator, or equivalently,…

Data-driven reduced order models (ROMs) are combined with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization.…

A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of…

In this paper we show how to construct diagonal scalings for arbitrary matrix pencils $\lambda B-A$, in which both $A$ and $B$ are complex matrices (square or nonsquare). The goal of such diagonal scalings is to "balance" in some sense the…

We consider a quadratic operator pencil with a small periodic perturbation multiplied by the spectral parameter. It is motivated, in particular, by a one-dimensional Klein-Gordon equation with a time-parity-symmetric perturbation. We study…

This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient…

We study Laplace eigenvalues $\lambda_k$ on K\"ahler manifolds as functionals on the space of K\"ahler metrics with cohomologous K\"ahler forms. We introduce a natural notion of a $\lambda_k$-extremal K\"ahler metric and obtain necessary…

The Lanczos algorithm, introduced by Cornelius Lanczos, has been known for a long time and is widely used in computational physics. While often employed to approximate extreme eigenvalues and eigenvectores of an operator, recently interest…