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Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…

Data Structures and Algorithms · Computer Science 2012-06-18 David Sontag , Talya Meltzer , Amir Globerson , Tommi S. Jaakkola , Yair Weiss

Approximate matrix multiplication with limited space has received ever-increasing attention due to the emergence of large-scale applications. Recently, based on a popular matrix sketching algorithm -- frequent directions, previous work has…

Machine Learning · Computer Science 2024-06-25 Yuanyu Wan , Lijun Zhang

In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…

Data Structures and Algorithms · Computer Science 2021-02-02 Juan Ignacio Mulero-Martínez

Fault tolerance is a major concern in distributed computational settings. In the classic master-worker setting, a server (the master) needs to perform some heavy computation which it may distribute to $m$ other machines (workers) in order…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-10-30 Keren Censor-Hillel , Yuka Machino , Pedro Soto

Karppa & Kaski (2019) proposed a novel ``broken" or ``opportunistic" matrix multiplication algorithm, based on a variant of Strassen's algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks.…

Data Structures and Algorithms · Computer Science 2024-09-05 David G. Harris

For certain industrial control applications an explicit function capturing the nontrivial trade-off between competing objectives in closed loop performance is not available. In such scenarios it is common practice to use the human innate…

Systems and Control · Electrical Eng. & Systems 2020-02-11 Alex. S. Ira , Chris Manzie , Iman Shames , Robert Chin , Dragan Nesic , Hayato Nakada , Takeshi Sano

We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…

Numerical Analysis · Mathematics 2011-06-01 J. Bailey , M. A. Iwen , C. V. Spencer

Herein we explore a dual tree algorithm for matrix multiplication of $A\in \mathbb{R}^{M\times D}$ and $B\in\mathbb{R}^{D\times N}$, very narrowly effective if the normalized rows of $A$ and columns of $B$, treated as vectors in…

Data Structures and Algorithms · Computer Science 2020-12-11 CNP Slagle , Lance Fortnow

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Data Structures and Algorithms · Computer Science 2020-03-19 Agniva Chowdhury , Palma London , Haim Avron , Petros Drineas

Serving large-scale machine learning (ML) models efficiently and with low latency has become challenging owing to increasing model size and complexity. Quantizing models can simultaneously reduce memory and compute requirements,…

This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…

Chemical Physics · Physics 2014-10-21 Jacob N. Sanders , Xavier Andrade , Alán Aspuru-Guzik

We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…

Data Structures and Algorithms · Computer Science 2018-07-20 Fedor V. Fomin , Petr A. Golovach , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

Optimization and Control · Mathematics 2023-05-05 Bharat Kumar , Deepmala , A. K. Das

Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-07-30 Mufakir Qamar Ansari , Mudabir Qamar Ansari

In this paper we consider parallel implementations of approximate multiplication of large matrices with exponential decay of elements. Such matrices arise in computations related to electronic structure calculations and some other fields of…

Numerical Analysis · Mathematics 2021-02-23 Anton G. Artemov

We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…

Numerical Analysis · Mathematics 2025-06-25 Jean-Guillaume Dumas , Clément Pernet , Alexandre Sedoglavic

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…

Numerical Analysis · Computer Science 2016-07-26 Grey Ballard , Austin R. Benson , Alex Druinsky , Benjamin Lipshitz , Oded Schwartz

Quantization is essential for Neural Network (NN) compression, reducing model size and computational demands by using lower bit-width data types, though aggressive reduction often hampers accuracy. Mixed Precision (MP) mitigates this…

Machine Learning · Computer Science 2025-05-20 Shmulik Markovich-Golan , Daniel Ohayon , Itay Niv , Yair Hanani

We propose different implementations of the sparse matrix--dense vector multiplication (\spmv{}) for finite fields and rings $\Zb/m\Zb$. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-09-09 Brice Boyer , Jean-Guillaume Dumas , Pascal Giorgi

In optimization routines used for on-line Model Predictive Control (MPC), linear systems of equations are usually solved in each iteration. This is true both for Active Set (AS) methods as well as for Interior Point (IP) methods, and for…

Optimization and Control · Mathematics 2014-01-08 Daniel Axehill