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This paper describes a set of rational filtering algorithms to compute a few eigenvalues (and associated eigenvectors) of non-Hermitian matrix pencils. Our interest lies in computing eigenvalues located inside a given disk, and the proposed…

Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…

The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…

Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…

In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…

In this paper, we discuss a novel higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems. Optimal a priori error estimates are derived for both the approximate eigenspace and…

The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given…

In this work, we combine Beyn's method and the recently developed recursive integral method (RIM) to propose a contour integral-based, region partitioning eigensolver for nonlinear eigenvalue problems. A new partitioning criterion is…

We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source…

We propose an algorithm for general nonlinear eigenvalue problems to compute physically relevant eigenvalues within a chosen contour. Eigenvalue information is explored by contour integration incorporating different weight functions. The…

Leveraging Transformer attention has led to great advancements in HDR deghosting. However, the intricate nature of self-attention introduces practical challenges, as existing state-of-the-art methods often demand high-end GPUs or exhibit…

The homogeneous second-order descent method (Zhang et al. 2025, Mathematics of Operations Research) was initially proposed for unconstrained optimisation problems. HSODM shows excellent performance with respect to the global complexity rate…

Contour integration schemes are a valuable tool for the solution of difficult interior eigenvalue problems. However, the solution of many large linear systems with multiple right hand sides may prove a prohibitive computational expense. The…

Solving large-scale Generalized Eigenvalue Problems (GEPs) is a fundamental yet computationally prohibitive task in science and engineering. As a promising direction, contour integral (CI) methods, such as the CIRR algorithm, offer an…

The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium sized Hermitian generalized…

Non-smoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitian matrix dependent on one parameter, both proven to be…

This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…

Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…

Fast Iterative Shrinking-Threshold Algorithm (FISTA) is a popular fast gradient descent method (FGM) in the field of large scale convex optimization problems. However, it can exhibit undesirable periodic oscillatory behaviour in some…

We propose an a posteriori error estimator for high-order $p$- or $hp$-finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for estimating the error in the approximation of an eigenvalue…