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Matrix multiplication algorithm

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Publications associées (31)

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Fabrication and Characterization of High Aspect Ratio Amorphous Silicon Based Microchannel Plates

Christophe Ballif, Nicolas Würsch, Janina Christine Isabelle Löffler, Samira Alexandra Frey, Mohammad Beygi

This contribution focuses on the fabrication and characterization of microchannel plates made of hydrogenated amorphous silicon (AMCPs). Flexible fabrication processes and the semi-conducting nature of amorphous silicon could give these detectors the advan ...

2021

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Rachid Guerraoui, El Mahdi El Mhamdi, Sébastien Louis Alexandre Rouault, Le Nguyen Hoang, Arsany Hany Abdelmessih Guirguis, Sadegh Farhadkhani

We study Byzantine collaborative learning, where n nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and f < n nodes can behave arbitrarily. We prove that collaborati ...

2021

A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

WILEY2021

Construction of optimal spectral methods in phase retrieval

Lenka Zdeborová, Florent Gérard Krzakala

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X⋆ from the (possibly noisy) observation of |ΦX⋆|, in which Φ is a matrix of size m×n. We consider a \emph{high-dimensional} setting whe ...

2021

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Daniel Kressner, Stefano Massei

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...

SIAM PUBLICATIONS2020

Recursive blocked algorithms for linear systems with Kronecker product structure

Daniel Kressner

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of g ...

SPRINGER2020

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a k x k submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix can a ...

ELSEVIER SCIENCE INC2020

ESSOP: Efficient and Scalable Stochastic Outer Product Architecture for Deep Learning

Irem Boybat Kara, Abu Sebastian

Deep neural networks (DNNs) have surpassed human-level accuracy in a variety of cognitive tasks but at the cost of significant memory/time requirements in DNN training. This limits their deployment in energy and memory limited applications that require rea ...

IEEE2020

Accurate Emulation of Memristive Crossbar Arrays for In-Memory Computing

Irem Boybat Kara

In-memory computing is an emerging non-von Neumann computing paradigm where certain computational tasks are performed in memory by exploiting the physical attributes of the memory devices. Memristive devices such as phase-change memory (PCM), where informa ...

IEEE2020

Phase retrieval in high dimensions: Statistical and computational phase transitions

Lenka Zdeborová, Florent Gérard Krzakala, Bruno Loureiro

We consider the phase retrieval problem of reconstructing a n -dimensional real or complex signal X ⋆ from m (possibly noisy) observations Y μ = | ∑ n i = 1 Φ μ i X ⋆ i / √ n | , for a large class of correlated real and complex random sensing matrices Φ , ...

Curran Associates, Inc.2020

Sub-Matrix Factorization for Real-Time Vote Prediction

Patrick Thiran, Matthias Grossglauser, Victor Kristof

We address the problem of predicting aggregate vote outcomes (e.g., national) from partial outcomes (e.g., regional) that are revealed sequentially. We combine matrix factorization techniques and generalized linear models (GLMs) to obtain a flexible, effic ...

2020