Related papers: Cucheb: A GPU implementation of the filtered Lancz…
For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues. The algorithm is based on the…
We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…
This article presents the principles, software architecture, and performance analysis of the GPU port of the lattice Boltzmann software library Palabos (J. Latt et al., "Palabos: Parallel lattice Boltzmann solver", Comput. Math. Appl. 81,…
Chebyshev filter diagonalization is well established in quantum chemistry and quantum physics to compute bulks of eigenvalues of large sparse matrices. Choosing a block vector implementation, we investigate optimization opportunities on the…
In recent years, applications such as real-time simulations, autonomous systems, and video games increasingly demand the processing of complex geometric models under stringent time constraints. Traditional geometric algorithms, including…
Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between…
This work introduces a method for determining the energy spectrum of lattice quantum chromodynamics (LQCD) by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to…
The Lanczos method with implicit restarting is one of the most popular methods for finding a few exterior eigenpairs of a large symmetric matrix $A$. Usually based on polynomial filtering, restarting is crucial to limit memory and the cost…
A thick-restart Lanczos type algorithm is proposed for Hermitian $J$-symmetric matrices. Since Hermitian $J$-symmetric matrices possess doubly degenerate spectra or doubly multiple eigenvalues with a simple relation between the degenerate…
In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…
Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from…
The low rank approximation of matrices is a crucial component in many data mining applications today. A competitive algorithm for this class of problems is the randomized block Lanczos algorithm - an amalgamation of the traditional block…
Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…
In her seminal 1989 work, Greenbaum demonstrated that the results produced by the finite precision Lanczos algorithm after $k$ iterations can be interpreted as exact Lanczos results applied to a larger matrix, whose eigenvalues lie in small…
Due to their flexibility and theoretical tractability Gaussian process (GP) regression models have become a central topic in modern statistics and machine learning. While the true posterior in these models is given explicitly, numerical…
We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of the Chebyshev-Davidson algorithm relies on the prior…
Heterogeneity in the cell population of cancer tissues poses many challenges in cancer diagnosis and treatment. Studying the heterogeneity in cell populations from gene expression measurement data in the context of cancer research is a…
GPCG is an algorithm within the Toolkit for Advanced Optimization (TAO) for solving bound constrained, convex quadratic problems. Originally developed by More' and Toraldo, this algorithm was designed for large-scale problems but had been…
We present GFORS, a GPU-accelerated framework for large binary integer programs. It couples a first-order (PDHG-style) routine that guides the search in the continuous relaxation with a randomized, feasibility-aware sampling module that…
We implement the Lanczos algorithm on an Intel Xeon Phi coprocessor and compare its performance to a multi-core Intel Xeon CPU and an NVIDIA graphics processor. The Xeon and the Xeon Phi are parallelized with OpenMP and the graphics…