Related papers: Solving singular generalized eigenvalue problems. …

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or…

Given a possibly singular matrix polynomial $P(z)$, we study how the eigenvalues, eigenvectors, root polynomials, minimal indices, and minimal bases of the pencils in the vector space $\mathbb{DL}(P)$ introduced in Mackey, Mackey, Mehl, and…

In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigenvectors. In this article we propose a new method for…

Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…

This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors…

Augmentation-based self-supervised learning methods have shown remarkable success in self-supervised visual representation learning, excelling in learning invariant features but often neglecting equivariant ones. This limitation reduces the…

Pole-swapping algorithms, which are generalizations of the QZ algorithm for the generalized eigenvalue problem, are studied. A new modular (and therefore more flexible) convergence theory that applies to all pole-swapping algorithms is…

This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…

By exploiting the connection between solving algebraic $\top$-Riccati equations and computing certain deflating subspaces of $\top$-palindromic matrix pencils, we obtain theoretical and computational results on both problems. Theoretically,…

This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel…

Inverse eigenvalue and singular value problems have been widely discussed for decades. The well-known result is the Weyl-Horn condition, which presents the relations between the eigenvalues and singular values of an arbitrary matrix. This…

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…

Unsupervised node representations learnt using contrastive learning-based methods have shown good performance on downstream tasks. However, these methods rely on augmentations that mimic low-pass filters, limiting their performance on tasks…

Uplift modeling is aimed at estimating the incremental impact of an action on an individual's behavior, which is useful in various application domains such as targeted marketing (advertisement campaigns) and personalized medicine (medical…

We describe two algorithms for the eigenvalue, eigenvector problem which, on input a Gaussian matrix with complex entries, finish with probability 1 and in average polynomial time.

We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The projection subspaces are constructed iteratively by means of…

In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan…

Quiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of vectors to vertices, of any finite-dimensional representation…

Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, and canonical correlation analysis are specific instances of…