Related papers: High-Performance Out-of-core Block Randomized Sing…
The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arithmetic, each update multiplies the running singular basis by…
Emulating computationally intensive scientific simulations is crucial for enabling uncertainty quantification, optimization, and informed decision-making at scale. Gaussian Processes (GPs) offer a flexible and data-efficient foundation for…
Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order…
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…
Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant…
In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous time levels leads to storage requirements that grow…
We study the convergence properties of the VR-PCA algorithm introduced by \cite{shamir2015stochastic} for fast computation of leading singular vectors. We prove several new results, including a formal analysis of a block version of the…
The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…
Vision-Language Models (VLMs) have revolutionized multi-modal learning by jointly processing visual and textual information. Yet, they face significant challenges due to the high computational and memory demands of processing long sequences…
In this paper, we propose a parallel block-based Viterbi decoder (PBVD) on the graphic processing unit (GPU) platform for the decoding of convolutional codes. The decoding procedure is simplified and parallelized, and the characteristic of…
Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms…
In this letter, we propose a simple yet effective singular value decomposition (SVD) based strategy to reduce the optimization problem dimension in data-enabled predictive control (DeePC). Specifically, in the case of linear time-invariant…
This article introduces randomized block Gram-Schmidt process (RBGS) for QR decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm and inherits its key characteristics such as being more efficient and having…
An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…
This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a…
The generalized singular value decomposition (GSVD, a.k.a. "SVD triplet", "duality diagram" approach) provides a unified strategy and basis to perform nearly all of the most common multivariate analyses (e.g., principal components,…
Tensor decomposition (TD) is an important method for extracting latent information from high-dimensional (multi-modal) sparse data. This study presents a novel framework for accelerating fundamental TD operations on massively parallel GPU…
This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the…
Spectral clustering and Singular Value Decomposition (SVD) are both widely used technique for analyzing graph data. In this note, I will present their connections using simple linear algebra, aiming to provide some in-depth understanding…
We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used…