Related papers: Cucheb: A GPU implementation of the filtered Lancz…
Selected inversion is essential for applications such as Bayesian inference, electronic structure calculations, and inverse covariance estimation, where computing only specific elements of large sparse matrix inverses significantly reduces…
Filters approximately store a set of items while trading off accuracy for space-efficiency and can address the limited memory on accelerators, such as GPUs. However, there is a lack of high-performance and feature-rich GPU filters as most…
The Lanczos method is one of the standard approaches for computing a few eigenpairs of a large, sparse, symmetric matrix. It is typically used with restarting to avoid unbounded growth of memory and computational requirements. Thick-restart…
The Lanczos method is a fast and memory-efficient algorithm for solving large-scale symmetric eigenvalue problems. However, its rapid convergence can deteriorate significantly when computing clustered eigenvalues due to a lack of cluster…
This paper proposes a harmonic Lanczos bidiagonalization method for computing some interior singular triplets of large matrices. It is shown that the approximate singular triplets are convergent if a certain Rayleigh quotient matrix is…
The Lanczos algorithm is evaluated for solving the time-independent as well as the time-dependent Dirac equation with arbitrary electromagnetic fields. We demonstrate that the Lanczos algorithm can yield very precise eigenenergies and…
As modern massively parallel clusters are getting larger with beefier compute nodes, traditional parallel eigensolvers, such as direct solvers, struggle keeping the pace with the hardware evolution and being able to scale efficiently due to…
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is…
Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods. In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and…
Models of quantum systems scale exponentially with the addition of single-particle states, which can present computationally intractable problems. Alternatively, quantum computers can store a many-body basis of $2^n$ dimensions on $n$…
This research proposes a practical method for detecting featureless objects by using image alignment approach with a robust similarity measure in industrial applications. This similarity measure is robust against occlusion, illumination…
A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos…
Graphics Processing Units (GPUs) with high computational capabilities used as modern parallel platforms to deal with complex computational problems. We use this platform to solve large-scale linear programing problems by revised simplex…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…
Bloom filters are a fundamental data structure for approximate membership queries, with applications ranging from data analytics to databases and genomics. Several variants have been proposed to accommodate parallel architectures. GPUs,…
GPUs have become indispensable in high-performance computing, machine learning, and many other domains. Efficiently utilizing the memory subsystem on GPUs is critical for maximizing computing power through massive parallelism. Analyzing…
This paper introduces cuHALLaR, a GPU-accelerated implementation of the HALLaR method proposed in Monteiro et al. 2024 for solving large-scale semidefinite programming (SDP) problems. We demonstrate how our Julia-based implementation…
In this paper, we demonstrate how GPU-accelerated BEM routines can be used in a simple black-box fashion to accelerate fast boundary element formulations based on Hierarchical Matrices (H-Matrices) with ACA (Adaptive Cross Approximation).…
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…