Related papers: GSoFa: Scalable Sparse Symbolic LU Factorization o…
In this paper, we propose a new regression-based algorithm to compute Graph Fourier Transform (GFT). Our algorithm allows different regularizations to be included when computing the GFT analysis components, so that the resulting components…
FFT (fast Fourier transform) plays a very important role in many fields, such as digital signal processing, digital image processing and so on. However, in application, FFT becomes a factor of affecting the processing efficiency, especially…
In this work, we present a new scalable incomplete LU factorization framework called Javelin to be used as a preconditioner for solving sparse linear systems with iterative methods. Javelin allows for improved parallel factorization on…
We propose two novel techniques for overcoming load-imbalance encountered when implementing so-called look-ahead mechanisms in relevant dense matrix factorizations for the solution of linear systems. Both techniques target the scenario…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…
The reduction of a banded matrix to bidiagonal form is a critical step in the calculation of Singular Values, a cornerstone of scientific computing and AI. Although inherently parallel, this step has traditionally been considered unsuitable…
The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…
Subgraph matching is a basic operation widely used in many applications. However, due to its NP-hardness and the explosive growth of graph data, it is challenging to compute subgraph matching, especially in large graphs. In this paper, we…
Low-rank matrix approximation is a fundamental tool in data analysis for processing large datasets, reducing noise, and finding important signals. In this work, we present a novel truncated LU factorization called Spectrum-Revealing LU…
Sparse matrix-vector multiplication (SpMV) operations are commonly used in various scientific applications. The performance of the SpMV operation often depends on exploiting regularity patterns in the matrix. Various representations have…
Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…
Large language models (LLMs) have demonstrated remarkable performance across a wide range of language processing tasks. However, this success comes at the cost of substantial computation and memory requirements, which significantly impedes…
We propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable…
Gr\"obner basis computation over multivariate polynomial rings remains one of the most powerful yet computationally hostile primitives in symbolic computation. While modern algorithms (Faug\`ere-type F4 and signature-based F5) reduce many…
This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many…
While existing algorithms may be used to solve a linear system over a general field in matrix-multiplication time, the complexity of constructing a symmetric triangular factorization (LDL) has received relatively little formal study. The…
Process mapping asks to assign vertices of a task graph to processing elements of a supercomputer such that the computational workload is balanced while the communication cost is minimized. Motivated by the recent success of GPU-based graph…
Currently, the size of scientific data is growing at an unprecedented rate. Data in the form of tensors exhibit high-order, high-dimensional, and highly sparse features. Although tensor-based analysis methods are very effective, the large…
Unsupervised integrative analysis of multiple data sources has become common place and scalable algorithms are necessary to accommodate ever increasing availability of data. Only few currently methods have estimation speed as their focus,…
Weight-Decomposed Low-Rank Adaptation (DoRA) extends LoRA by decoupling weight magnitude from direction, but its forward pass requires the row-wise norm of W + sBA, a computation that every major framework we surveyed implements by…