相关论文: Computing eigenfunctions and eigenvalues of bounda…

A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…

We present an application of a nonstandard approximate method---the finite-rank approximation---to solving the time-independent Schr\"odinger equation for a bound-state problem. The method is illustrated on the example of a…

The stationary, axisymmetric reduction of the vacuum Einstein equations, the so-called Ernst equation, is an integrable nonlinear PDE in two dimensions. There now exists a general method for analyzing boundary value problems for integrable…

By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…

Recently, a non-classical eigenvalue solver, called RIM, was proposed to compute (all) eigenvalues in a region on the complex plane. Without solving any eigenvalue problem, it tests if a region contains eigenvalues using an approximate…

This paper is concerned with the Taylor-reduced basis method (Taylor-RBM) for the efficient approximation of eigenspaces of large scale parametric Hermitian matrices. The Taylor-RBM is a local model order reduction method, which constructs…

Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…

In this paper we propose and analyze spectral-Galerkin methods for the Stokes eigenvalue problem based on the stream function formulation in polar geometries. We first analyze the stream function} formulated fourth-order equation under the…

We introduce a hybrid high-order method for approximating the ground state of the nonlinear Gross--Pitaevskii eigenvalue problem. Optimal convergence rates are proved for the ground state approximation, as well as for the associated…

We propose a numerical method for evaluating eigenvalues and eigenfunctions of Schr\"odinger operators with general confining potentials. The method is selective in the sense that only the eigenvalue closest to a chosen input energy is…

In this paper, we present Gauss's law-preserving spectral methods and their efficient solution algorithms for curl-curl source and eigenvalue problems in two and three dimensions arising from Maxwell's equations. Arbitrary order…

Super-resolution (SR) with arbitrary scale factor and cost-and-quality controllability at test time is essential for various applications. While several arbitrary-scale SR methods have been proposed, these methods require us to modify the…

An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…

We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as…

A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…

Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this…

We consider the problem of recovering the superposition of $R$ distinct complex exponential functions from compressed non-uniform time-domain samples. Total Variation (TV) minimization or atomic norm minimization was proposed in the…

Recently, stochastic rounding (SR) has been implemented in specialized hardware but most current computing nodes do not yet support this rounding mode. Several works empirically illustrate the benefit of stochastic rounding in various…

Spectral parameter power series (SPPS) method is a recently introduced technique for solving linear differential equations and related spectral problems. In the present work we develop an approach based on the SPPS for analysis of…

Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…