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We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} =…

Numerical Analysis · Computer Science 2018-03-01 Jean-Guillaume Dumas , Clement Pernet

We introduce a fully convolutional fractional scaling component, FCFS. Fully convolutional networks can be applied to any size input and previously did not support non-integer scaling. Our architecture is simple with an efficient single…

Neural and Evolutionary Computing · Computer Science 2022-03-22 Michael Soloveitchik , Michael Werman

Cholesky linear solvers are a critical bottleneck in challenging applications within computer graphics and scientific computing. These applications include but are not limited to elastodynamic barrier methods such as Incremental Potential…

Numerical Analysis · Mathematics 2025-07-04 Behrooz Zarebavani , Danny M. Kaufman , David I. W. Levin , Maryam Mehri Dehnavi

In the field of digital signal processing, the fast Fourier transform (FFT) is a fundamental algorithm, with its processors being implemented using either the pipelined architecture, well-known for high-throughput applications but weak in…

Hardware Architecture · Computer Science 2025-01-03 Fangyu Zhao , Chunhua Xiao , Zhiguo Wang , Xiaohua Du , Bo Dong

In inverting large sparse matrices, the key difficulty lies in effectively exploiting sparsity during the inversion process. One well-established strategy is the nested dissection, which seeks the so-called sparse Cholesky factorization. We…

Numerical Analysis · Mathematics 2025-05-14 Michał Kos , Krzysztof Podgórski , Hanqing Wu

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…

Numerical Analysis · Computer Science 2016-05-09 Yuan Lu , Jie Yang

We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…

Numerical Analysis · Mathematics 2026-02-27 Pei-Chun Su , Ronald R. Coifman

A new format for storing sparse matrices is proposed for efficient sparse matrix-vector (SpMV) product calculation on modern graphics processing units (GPUs). This format extends the standard compressed row storage (CRS) format and can be…

Computational Physics · Physics 2014-04-29 Zbigniew Koza , Maciej Matyka , Sebastian Szkoda , Łukasz Mirosław

BLASFEO is a dense linear algebra library providing high-performance implementations of BLAS- and LAPACK-like routines for use in embedded optimization and other applications targeting relatively small matrices. BLASFEO defines an API which…

Mathematical Software · Computer Science 2020-06-09 Gianluca Frison , Tommaso Sartor , Andrea Zanelli , Moritz Diehl

Numeric modeling of electromagnetics and acoustics frequently entails matrix-vector multiplication with block Toeplitz structure. When the corresponding block Toeplitz matrix is not highly sparse, e.g. when considering the electromagnetic…

Numerical Analysis · Mathematics 2024-06-27 Alexandre Siron , Sean Molesky

In this paper, an optimized efficient VLSI architecture of a pipeline Fast Fourier transform (FFT) processor capable of producing the reverse output order sequence is presented. Paper presents Radix-2 multipath delay architecture for FFT…

Hardware Architecture · Computer Science 2017-07-07 Tanaji U. Kamble , B. G. Patil , Rakhee S. Bhojakar

Non-negative matrix factorization (NMF) is a popular unsupervised learning approach widely used in image clustering. However, in real-world clustering scenarios, most existing NMF methods are highly sensitive to noise corruption and are…

Computer Vision and Pattern Recognition · Computer Science 2025-05-01 Jingjing Liu , Nian Wu , Xianchao Xiu , Jianhua Zhang

As a prevalent distributed learning paradigm, Federated Learning (FL) trains a global model on a massive amount of devices with infrequent communication. This paper investigates a class of composite optimization and statistical recovery…

Machine Learning · Computer Science 2022-10-04 Yajie Bao , Michael Crawshaw , Shan Luo , Mingrui Liu

The parallel algorithm for loading large sparse matrices from files into distributed memories of high performance computing (HPC) systems is presented. This algorithm was designed specially for matrices stored in files in the space-effcient…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-12-30 Daniel Langr , Ivan Šimeček , Pavel Tvrdík

The graph Laplacian is a standard tool in data science, machine learning, and image processing. The corresponding matrix inherits the complex structure of the underlying network and is in certain applications densely populated. This makes…

Machine Learning · Computer Science 2018-12-13 Dominik Alfke , Daniel Potts , Martin Stoll , Toni Volkmer

We present a new method for performing global redistributions of multidimensional arrays essential to parallel fast Fourier (or similar) transforms. Traditional methods use standard all-to-all collective communication of contiguous memory…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-04-26 Lisandro Dalcin , Mikael Mortensen , David E Keyes

Tile low rank representations of dense matrices partition them into blocks of roughly uniform size, where each off-diagonal tile is compressed and stored as its own low rank factorization. They offer an attractive representation for many…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-08-27 Wajih Boukaram , Stefano Zampini , George Turkiyyah , David Keyes

Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…

Machine Learning · Computer Science 2016-05-04 Mariano Tepper , Guillermo Sapiro

A low-latency and energy-efficient tensor algebra accelerator design must optimize how data movement and operations are scheduled (i.e., mapped) in the accelerator architecture. A key mapping optimization is fusion, meaning holding data…

Hardware Architecture · Computer Science 2026-05-05 Tanner Andrulis , Michael Gilbert , Vivienne Sze , Joel S. Emer

Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…

Machine Learning · Statistics 2020-01-28 Kaiyi Ji , Jian Tan , Jinfeng Xu , Yuejie Chi