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

Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes…

We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…

In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…

The harmonic Lanczos bidiagonalization method can be used to compute the smallest singular triplets of a large matrix $A$. We prove that for good enough projection subspaces harmonic Ritz values converge if the columns of $A$ are strongly…

In this paper, we consider an $\ell_{0}$-norm penalized formulation of the generalized eigenvalue problem (GEP), aimed at extracting the leading sparse generalized eigenvector of a matrix pair. The formulation involves maximization of a…

In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue…

We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…

Spectral methods are widely used in geometry processing of 3D models. They rely on the projection of the mesh geometry on the basis defined by the eigenvectors of the graph Laplacian operator, becoming computationally prohibitive as the…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of…

We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, associated with the Neumann Laplacian in a box $\Omega\subset\mathbb{R}^N$, which arises in the investigation of the survival threshold in…

Hyperspectral images (HSI) contain a wealth of information over hundreds of contiguous spectral bands, making it possible to classify materials through subtle spectral discrepancies. However, the classification of this rich spectral…

Many problems of interest in computer vision can be formulated as a problem of finding consistent correspondences between two feature sets. Feature correspondence (matching) problem with one-to-one mapping constraint is usually formulated…

This paper looks at the tensor eigenvalue complementarity problem (TEiCP) which arises from the stability analysis of finite dimensional mechanical systems and is closely related to the optimality conditions for polynomial optimization. We…

We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number $\kappa$ in bounded domains in $\mathbb{R}^d$. The discrete trial and test spaces are generated from…

Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis (PCA) and the calculation of truncated singular value decompositions (SVD). The present…

The Bethe-Salpeter eigenvalue problem is a structured eigenvalue problem arising in many-body physics. In practice, a few of the smallest positive eigenvalues and the corresponding eigenvectors need to be computed. In principle, the LOBPCG…

We revisit the $k$-Hessian eigenvalue problem on a smooth, bounded, $(k-1)$-convex domain in $\mathbb R^n$. First, we obtain a spectral characterization of the $k$-Hessian eigenvalue as the infimum of the first eigenvalues of linear…

As the number of model parameters increases, parameter-efficient fine-tuning (PEFT) has become the go-to choice for tailoring pre-trained large language models. Low-rank Adaptation (LoRA) uses a low-rank update method to simulate full…

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…