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We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…

Numerical Analysis · Mathematics 2021-11-18 João R. Cardoso , Amir Sadeghi

Coded computation is a method to mitigate "stragglers" in distributed computing systems through the use of error correction coding that has lately received significant attention. First used in vector-matrix multiplication, the range of…

Information Theory · Computer Science 2018-06-28 Nuwan Ferdinand , Stark Draper

Inefficient data transfer between computation and memory inspired emerging processing-in-memory (PIM) technologies. Many PIM solutions enable storage and processing using memristors in a crossbar-array structure, with techniques such as…

Hardware Architecture · Computer Science 2021-05-11 Orian Leitersdorf , Ben Perach , Ronny Ronen , Shahar Kvatinsky

Computationally efficient matrix multiplication is a fundamental requirement in various fields, including and particularly in data analytics. To do so, the computation task of a large-scale matrix multiplication is typically outsourced to…

Information Theory · Computer Science 2018-11-01 Jaber Kakar , Seyedhamed Ebadifar , Aydin Sezgin

Many kernel methods suffer from high time and space complexities and are thus prohibitive in big-data applications. To tackle the computational challenge, the Nystr\"om method has been extensively used to reduce time and space complexities…

Machine Learning · Computer Science 2014-04-02 Shusen Wang , Zhihua Zhang

Coded computation techniques provide robustness against straggling workers in distributed computing. However, most of the existing schemes require exact provisioning of the straggling behaviour and ignore the computations carried out by…

Information Theory · Computer Science 2021-12-07 Emre Ozfatura , Sennur Ulukus , Deniz Gunduz

The flip graph algorithm is a method for discovering new matrix multiplication schemes by following random walks on a graph. We introduce a version of the flip graph algorithm for matrix multiplication schemes that admit certain symmetries.…

Symbolic Computation · Computer Science 2025-02-10 Jakob Moosbauer , Michael Poole

Two primary challenges stand in the way of practical large-scale quantum computation, namely achieving sufficiently low error rate quantum gates and implementing interesting quantum algorithms with a physically reasonable number of qubits.…

Quantum Physics · Physics 2013-04-10 Austin G. Fowler , Simon J. Devitt

Much attention has been given to the efficient computation of pairings on elliptic curves with even embedding degree since the advent of pairing-based cryptography. The few existing works in the case of odd embedding degrees require some…

Algebraic Geometry · Mathematics 2023-06-22 Emmanuel Fouotsa , Nadia El Mrabet , Aminatou Pecha

Elliptic curves over finite fields GF(2^n) play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this…

Quantum Physics · Physics 2013-12-05 Brittanney Amento , Rainer Steinwandt , Martin Roetteler

Many emerging computer applications require the processing of large numbers, larger than what a CPU can handle. In fact, the top of the line PCs can only manipulate numbers not longer than 32 bits or 64 bits. This is due to the size of the…

Data Structures and Algorithms · Computer Science 2012-04-03 Youssef Bassil , Aziz Barbar

As post-quantum cryptography (PQC) becomes increasingly critical for securing future communication systems, the performance overhead introduced by quantum-resistant algorithms presents a major computing challenge. HQC (Hamming Quasi-Cyclic)…

Cryptography and Security · Computer Science 2025-12-16 Ben Dong , Hui Feng , Qian Wang

Matrix multiplication is a very important computation kernel both in its own right as a building block of many scientific applications and as a popular representative for other scientific applications. Cannon algorithm which dates back to…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-06-19 Jean-Noel Quintin , Khalid Hasanov , Alexey Lastovetsky

Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introduced in a typical high school algebra course yet in practice…

Mathematical Software · Computer Science 2016-09-02 Jianyu Huang , Robert A. van de Geijn

The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of…

Machine Learning · Computer Science 2020-04-29 Hufei Zhu

The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…

Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based…

Quantum Physics · Physics 2025-10-28 Quan Gu , Han Ye , Junjie Chen , Xiongfeng Ma

A cryptarithm (or alphametic) is a mathematical puzzle in which numbers are represented with words in such a way that identical letters stand for equal digits and distinct letters for unequal digits. An alphametic puzzle is usually given in…

Number Theory · Mathematics 2025-08-29 Dmytro S. Inosov , Emil Vlasák

We present an algorithm that, on input of a positive integer N together with its prime factorization, constructs a finite field F and an elliptic curve E over F for which E(F) has order N. Although it is unproved that this can be done for…

Number Theory · Mathematics 2007-05-23 Reinier Broker , Peter Stevenhagen

In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-04-19 Sinong Wang , Jiashang Liu , Ness Shroff