相关论文: FEAST as a Subspace Iteration Eigensolver Accelera…

Most iterative algorithms for eigenpair computation consist of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz (RR) projection step that extracts approximate…

The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This new scheme is derived from a…

Fully Homomorphic Encryption (FHE) is a set of powerful cryptographic schemes that allows computation to be performed directly on encrypted data with an unlimited depth. Despite FHE's promising in privacy-preserving computing, yet in most…

Hierarchical text classification (HTC) and extreme multi-label classification (XML) tasks face compounded challenges from complex label interdependencies, data sparsity, and extreme output dimensions. These challenges are exemplified in the…

Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters…

Studying the optoelectronic structure of materials can require the computation of several thousands of the smallest positive eigenpairs of a pseudo-hermitian Hamiltonian. Iterative eigensolvers may be preferred over direct methods for this…

An efficient contour integral technique to approximate a cluster of nonlinear eigenvalues of a polynomial eigenproblem, circumventing certain large inversions from a linearization, is presented. It is applied to the nonlinear eigenproblem…

Recently, single-frame infrared small target (SIRST) detection technology has attracted widespread attention. Different from most existing deep learning-based methods that focus on improving network architectures, we propose a…

This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix $A(\mu)$ for many parameter values $\mu \in \mathbb{R}^P$. The design of reliable and efficient algorithms for addressing this task…

This paper presents a new major release of the program FIESTA (Feynman Integral Evaluation by a Sector decomposiTion Approach). The new release is mainly aimed at optimal performance at large scales when one is increasing the number of…

We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…

This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…

Incremental learning aims to adapt to new sets of categories over time with minimal computational overhead. Prior work often addresses this task by training efficient task-specific adaptors that modify frozen layer weights or features to…

This paper provides a new way of developing the fast iterative shrinkage/thresholding algorithm (FISTA) that is widely used for minimizing composite convex functions with a nonsmooth term such as the $\ell_1$ regularizer. In particular,…

The use of Green's function in quantum many-body theory often leads to nonlinear eigenvalue problems, as Green's function needs to be defined in energy domain. The $GW$ approximation method is one of the typical examples. In this article,…

Spatial Transcriptomics (ST) provides spatially-resolved gene expression, offering crucial insights into tissue architecture and complex diseases. However, its prohibitive cost limits widespread adoption, leading to significant attention on…

Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…

Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…

Subspace methods are commonly used for finding approximate eigenvalues and singular values of large-scale matrices. Once a subspace is found, the Rayleigh-Ritz method (for symmetric eigenvalue problems) and Petrov-Galerkin projection (for…