Related papers: A hierarchically blocked Jacobi SVD algorithm for …
We propose a novel unifying scheme for parallel implementation of articulated robot dynamics algorithms. It is based on a unified Lie group notation for deriving the equations of motion of articulated robots, where various well-known…
Mining large graphs for information is becoming an increasingly important workload due to the plethora of graph structured data becoming available. An aspect of graph algorithms that has hitherto not received much interest is the effect of…
Distributed-memory implementations of numerical optimization algorithm, such as stochastic gradient descent (SGD), require interprocessor communication at every iteration of the algorithm. On modern distributed-memory clusters where…
Three refined and refined harmonic extraction-based Jacobi--Davidson (JD) type methods are proposed, and their thick-restart algorithms with deflation and purgation are developed to compute several generalized singular value decomposition…
In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (R3SVD) algorithm is used to adaptively carry out partial…
Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…
In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…
Graph Neural Networks (GNNs) have shown excellent performance on graphs that exhibit strong homophily with respect to the node labels i.e. connected nodes have same labels. However, they perform poorly on heterophilic graphs. Recent…
This paper investigates the multi-GPU performance of a 3D buoyancy driven cavity solver using MPI and OpenACC directives on different platforms. The paper shows that decomposing the total problem in different dimensions affects the strong…
Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…
High-dimensional image data often require dimensionality reduction before further analysis. This paper provides a purely analytical comparison of two linear techniques-Principal Component Analysis (PCA) and Singular Value Decomposition…
This thesis gives an overview of the state-of-the-art randomized linear algebra algorithms for singular value decomposition (SVD), including the presentation of existing pseudo-codes and theoretical error analysis. Our main focus is on…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…
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…
We present a shared-memory algorithm to compute high-quality solutions to the balanced $k$-way hypergraph partitioning problem. This problem asks for a partition of the vertex set into $k$ disjoint blocks of bounded size that minimizes the…
This paper is devoted to proposing a general weighted low-rank recovery model and designing a fast SVD-free computational scheme to solve it. First, our generic weighted low-rank recovery model unifies several existing approaches in the…
We make a convergence analysis of the harmonic and refined harmonic extraction versions of Jacobi-Davidson SVD (JDSVD) type methods for computing one or more interior singular triplets of a large matrix $A$. At each outer iteration of these…
Estimating singular subspaces from noisy matrices is a fundamental problem with wide-ranging applications across various fields. Driven by the challenges of data integration and multi-view analysis, this study focuses on estimating shared…
The structured singular value (SSV), or mu, is used to assess the robust stability and performance of an uncertain linear time-invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that…