相关论文: A Novel Skew-Hamiltonian Isotropic Lanczos Algorit…

Optimally hybrid numerical solvers were constructed for massively parallel generalized eigenvalue problem (GEP).The strong scaling benchmark was carried out on the K computer and other supercomputers for electronic structure calculation…

Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace--Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The…

The analysis of the acceleration behavior of gradient-based eigensolvers with preconditioning presents a substantial theoretical challenge. In this work, we present a novel framework for preconditioning on Riemannian manifolds and introduce…

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for…

We consider a problem in eigenvalue optimization, in particular finding a local minimizer of the spectral abscissa - the value of a parameter that results in the smallest value of the largest real part of the spectrum of a matrix system.…

In this paper, a spectral method based on conformal mappings is proposed to solve Steklov eigenvalue problems and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov…

We prove the existence of optimal metrics for a wide class of combinations of Laplace eigenvalues on closed orientable surfaces of any genus. The optimal metrics are explicitely related to Laplace minimal eigenmaps, defined as branched…

We address an algorithm for the least squares fitting of a subset of the eigenvalues of an unknown Hermitian matrix lying an an affine subspace, called the Lift and Projection (LP) method, due to Chen and Chu (SIAM Journal on Numerical…

A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant…

The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy,…

This paper describes the software package Cucheb, a GPU implementation of the filtered Lanczos procedure for the solution of large sparse symmetric eigenvalue problems. The filtered Lanczos procedure uses a carefully chosen polynomial…

Principal components computed via PCA (principal component analysis) are traditionally used to reduce dimensionality in genomic data or to correct for population stratification. In this paper, we explore the penalized eigenvalue problem…

Image restoration and spectral reconstruction are longstanding computer vision tasks. Currently, CNN-transformer hybrid models provide state-of-the-art performance for these tasks. The key common ingredient in the architectural designs of…

In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its…

In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…

Dimensionality reduction, cluster analysis, and sparse representation are basic components in machine learning. However, their relationships have not yet been fully investigated. In this paper, we find that the spectral graph theory…

We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs)…

We use the refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems $({Ku=\lambda Mu})$. The rIGA framework conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) discretizations while…

We present a high-order shifted Gegenbauer pseudospectral method (SGPM) to solve numerically the second-order one-dimensional hyperbolic telegraph equation provided with some initial and Dirichlet boundary conditions. The framework of the…

We propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned matrices. It is based on the {\it LDLT} decomposition and involves finding a $k \times k$ sub-matrix of the inverse of the…