Related papers: Reducing Memory Cost of Exact Diagonalization usin…
We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of…
We present a Lanczos algorithm utilizing multiple grids that reduces the memory requirements both on disk and in working memory by one order of magnitude for RBC/UKQCD's 48I and 64I ensembles at the physical pion mass. The precision of the…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…
The block Lanczos algorithm proposed by Peter Montgomery is an efficient means to tackle the sparse linear algebra problem which arises in the context of the number field sieve factoring algorithm and its predecessors. We present here a…
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…
A fast non-convex low-rank matrix decomposition method for potential field data separation is proposed. The singular value decomposition of the large size trajectory matrix, which is also a block Hankel matrix, is obtained using a fast…
In this work we introduce a memory-efficient method for computing the action of a Hermitian matrix function on a vector. Our method consists of a rational Lanczos algorithm combined with a basis compression procedure based on rational…
Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank…
We investigate the solution of low-rank matrix approximation problems using the truncated SVD. For this purpose, we develop and optimize GPU implementations for the randomized SVD and a blocked variant of the Lanczos approach. Our work…
We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…
We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication…
The increasing imbalance between the computing capabilities of individual nodes and the internode bandwidth makes it highly desirable for any Lattice QCD algorithm to minimize the amount of internode communication. One of the relatively new…
We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster…
This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD).…
Recent years have witnessed the popularity of using rank minimization as a regularizer for various signal processing and machine learning problems. As rank minimization problems are often converted to nuclear norm minimization (NNM)…
We propose an efficient, distributed, out-of-memory implementation of the truncated singular value decomposition (t-SVD) for heterogeneous (CPU+GPU) high performance computing (HPC) systems. Various implementations of SVD have been…
We solve the Hubbard model with the exact diagonalization method on a graphics processing unit (GPU). We benchmark our GPU program against a sequential CPU code by using the Lanczos algorithm to solve the ground state energy in two cases: a…
Although support vector machines (SVMs) are theoretically well understood, their underlying optimization problem becomes very expensive, if, for example, hundreds of thousands of samples and a non-linear kernel are considered. Several…
This article presents svds-C, an open-source and high-performance C program for accurately and robustly computing truncated SVD, e.g. computing several largest singular values and corresponding singular vectors. We have re-implemented the…
Current bundle adjustment solvers such as the Levenberg-Marquardt (LM) algorithm are limited by the bottleneck in solving the Reduced Camera System (RCS) whose dimension is proportional to the camera number. When the problem is scaled up,…