Related papers: Inexact Krylov Subspace Algorithms for Large Matri…
Exploratory data analysis (EDA), coupled with SQL, is essential for data analysts involved in data exploration and analysis. However, data analysts often encounter two primary challenges: (1) the need to craft SQL queries skillfully, and…
Labeled Latent Dirichlet Allocation (LLDA) is an extension of the standard unsupervised Latent Dirichlet Allocation (LDA) algorithm, to address multi-label learning tasks. Previous work has shown it to perform in par with other…
This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…
In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations. The first approach is…
We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single…
We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale…
Electromigration (EM) induced stress evolution is a major reliability challenge in nanometer-scale VLSI interconnects. Accurate EM analysis requires solving stress-governing partial differential equations over large interconnect trees,…
In the past few decades, researchers have proposed many discriminant analysis (DA) algorithms for the study of high-dimensional data in a variety of problems. Most DA algorithms for feature extraction are based on transformations that…
In this paper a new restarting method for Krylov subspace matrix exponential evaluations is proposed. Since our restarting technique essentially employs the residual, some convergence results for the residual are given. We also discuss how…
Thanks to its great potential in reducing both computational cost and memory requirements, combining sketching and Krylov subspace techniques has attracted a lot of attention in the recent literature on projection methods for linear…
We study structure-preserving Krylov subspace methods for approximating the matrix-vector products f(H)b, where H is a large Hamiltonian matrix and f denotes either the matrix exponential or the related phi-function. Such computations are…
This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of…
The conventional supervised hashing methods based on classification do not entirely meet the requirements of hashing technique, but Linear Discriminant Analysis (LDA) does. In this paper, we propose to perform a revised LDA objective over…
An accurate residual--time (AccuRT) restarting for computing matrix exponential actions of nonsymmetric matrices by the shift-and-invert (SAI) Krylov subspace method is proposed. The proposed restarting method is an extension of the…
Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and data classification. In this paper, we present a quantum algorithm and a quantum circuit to efficiently perform linear…
Representation learning has become an effective technique utilized by electronic design automation (EDA) algorithms, which leverage the natural representation of workflow elements as images, grids, and graphs. By addressing challenges…
Applications such as face recognition that deal with high-dimensional data need a mapping technique that introduces representation of low-dimensional features with enhanced discriminatory power and a proper classifier, able to classify…
We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a…
We develop a novel convergence analysis of the classical deterministic block Krylov methods for the approximation of $h$-dimensional dominant subspaces and low-rank approximations of matrices $ A\in\mathbb K^{m\times n}$ (where $\mathbb…
We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an…