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Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of…

Mathematical Software · Computer Science 2020-01-22 Wayne B. Mitchell , Robert Strzodka , Robert D. Falgout

In LoRa (Long Range), when a collision occurs in the network, each end-device has to retransmit its colliding frame, which reduces the throughput, and increases the energy consumption of the end-devices and the delay of the frames. In this…

Networking and Internet Architecture · Computer Science 2019-02-15 Samira Abboud , Nancy El Rachkidy , Alexandre Guitton

We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new…

Information Theory · Computer Science 2015-02-25 Alexey Frolov , Victor Zyablov

As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key…

Quantum Physics · Physics 2020-09-21 James R. Cruise , Neil I. Gillespie , Brendan Reid

Large language model inference is both memory-intensive and time-consuming, often requiring distributed algorithms to efficiently scale. Various model parallelism strategies are used in multi-gpu training and inference to partition…

This paper presents a fault-tolerant algorithm for the QR factorization of general matrices. It relies on the communication-avoiding algorithm, and uses the structure of the reduction of each part of the computation to introduce…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-15 Camille Coti

The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…

Data Structures and Algorithms · Computer Science 2011-09-12 Grey Ballard , James Demmel , Olga Holtz , Oded Schwartz

For finite geometry low-density parity-check codes, heavy row and column weights in their parity check matrix make the decoding with even Min-Sum (MS) variants computationally expensive. To alleviate it, we present a class of hybrid schemes…

Information Theory · Computer Science 2009-07-02 Guangwen Li , Dashe Li , Yuling Wang , Wenyan Sun

Inference for Large Language Models (LLMs) is computationally demanding. To reduce the cost of auto-regressive decoding, Key-Value (KV) cache is used to store intermediate activations, which significantly lowers the computational overhead…

Machine Learning · Computer Science 2025-06-05 Chaoyi Jiang , Lei Gao , Hossein Entezari Zarch , Murali Annavaram

Large transformer models, such as BERT, achieve state-of-the-art results in machine reading comprehension (MRC) for open-domain question answering (QA). However, transformers have a high computational cost for inference which makes them…

Computation and Language · Computer Science 2021-08-06 Haytham ElFadeel , Stan Peshterliev

With endless amounts of data and very limited bandwidth, fast data compression is one solution for the growing datasharing problem. Compression helps lower transfer times and save memory, but if the compression takes too long, this no…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-06-21 David Noel , Elizabeth Graham , Liyuan Liu

System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Valentin Nedelcu , Ioan Dumitrache

We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…

Symbolic Computation · Computer Science 2019-06-04 Mohammadali Asadi , Alexander Brandt , Robert H. C. Moir , Marc Moreno Maza , Yuzhen Xie

Achieving high image quality is an important aspect in an increasing number of wireless multimedia applications. These applications require resource efficient error correction hardware to detect and correct errors introduced by the…

Information Theory · Computer Science 2013-08-02 Vikram Arkalgud Chandrasetty , Syed Mahfuzul Aziz

Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling…

Numerical Analysis · Mathematics 2023-08-25 Matthias Mayr , Alexander Popp

We address the communication overhead of distributed sparse matrix-(multiple)-vector multiplication in the context of large-scale eigensolvers, using filter diagonalization as an example. The basis of our study is a performance model which…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-11-27 Andreas Alvermann , Georg Hager , Holger Fehske

The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…

Computational Complexity · Computer Science 2018-11-20 Lijie Chen , Ruosong Wang

All Lossy compression algorithms employ similar compression schemes -- frequency domain transform followed by quantization and lossless encoding schemes. They target tradeoffs by quantizating high frequency data to increase compression…

Information Theory · Computer Science 2021-12-15 Johnathan Chiu

Modern distributed training of machine learning models suffers from high communication overhead for synchronizing stochastic gradients and model parameters. In this paper, to reduce the communication complexity, we propose \emph{double…

Optimization and Control · Mathematics 2019-05-28 Yue Yu , Jiaxiang Wu , Longbo Huang

In this paper we present an optimized parallel implementation of a flexible MAP decoder for synchronization error correcting codes, supporting a very wide range of code sizes and channel conditions. On mid-range GPUs we demonstrate decoding…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-02-26 Johann A. Briffa