11 papers · ranked by Valyu relevance
Amal Altamimi, Belgacem Ben Youssef
The square root operation is indispensable in a myriad of computational science and engineering applications. Various computational techniques have been devised to approximate its value. In particular, convergence methods employed in this regard are highly affected by the initial approximation of the seed value.…
Mayer Goldberg
This work presents and extends a known spigot-algorithm for computing square-roots, digit-by-digit, that is suitable for calculation by hand or an abacus, using only addition and subtraction. We offer an elementary proof of correctness for the original algorithm, then present a corresponding spigot-algorithm for…
Ebru Adiguzel-Goktas, Enver Özdemir
In this paper, we present a review of three widely-used practical square root algorithms. We then describe a unifying framework where each of these well-known algorithms can be seen as a special case of it. The framework with singular curves offers a broad perspective to compare and further improve the existing methods…
Fábio Lourenço Romano
numbers, using floating-point arithmetic Authors: ['Fábio Lourenço Romano'] In this paper, an optimized version of classical Bombelli's algorithm for computing integer square roots is presented. In particular, floating-point arithmetic is used to compute the initial guess of each digit of the root, following similar…
Amal Altamimi, Belgacem Ben Youssef, Oleg Sergiyenko, Wendy Flores-Fuentes + 2 more
'Wendy Flores-Fuentes' 'Julio Cesar Rodríguez-Quiñonez' 'Jesús Elías Miranda-Vega'] Rapid and continuous advancements in remote sensing technology have resulted in finer resolutions and higher acquisition rates of hyperspectral images (HSIs). These developments have triggered a need for new processing techniques…
Zofia Długosz, Michał Rajewski, Rafał Długosz, Tomasz Talaśka + 1 more
'Adam Krzyzak'] In this work, we propose a novel metaheuristic algorithm that evolved from a conventional particle swarm optimization (PSO) algorithm for application in miniaturized devices and systems that require low energy consumption. The modifications allowed us to substantially reduce the computational complexity…
Yann Dijoux
roots Authors: ['Yann Dijoux'] Abstract. The Householder's method is a root-find algorithm which is a natural extension of the methods of Newton and Halley. The current paper mostly focuses on approximating the square root of a positive real number based on these methods. The resulting algorithms can be expressed using…
Amal Altamimi, Belgacem Ben Youssef, Luca Di Nunzio, Sergio Spanò
Recent advancements in hyperspectral imaging have significantly increased the acquired data volume, creating a need for more efficient compression methods for handling the growing storage and transmission demands. These challenges are particularly critical for onboard satellite systems, where power and computational…
Muhammad Usman, Javed Iqbal, Alamgir Khan, Ikram Ullah + 3 more
'Jehad Alzabut' 'Hisham Mohammad Alkhawar'] This study introduces an advanced iterative technique designed to solve nonlinear equations with simple roots efficiently. The newly developed algorithm achieves an impressive convergence order of sixteen, utilizing only five functional evaluations per iteration. By…
Ankur Changela, Yogesh Kumar, Marcin Woźniak, Jana Shafi + 1 more
'Muhammad Fazal Ijaz'] In this article, a low-complexity VLSI architecture based on a radix-4 hyperbolic COordinate Rotion DIgital Computer (CORDIC) is proposed to compute the $N{{\rm th}}$ root and $N{{\rm th}}$ power of a fixed-point number. The most recent techniques use the radix-2 CORDIC algorithm to compute the…
Nuh Aydin, Mohammad K. Azarian, Omid Khormali, Ghaya Mtimet
The square-and-multiply algorithm, also known as binary exponentiation or repeated squaring, is a technique for fast exponentiation commonly used in modern cryptography and computational number theory. Despite its prominence, the historical origins of the algorithm are not known with certainty. This paper critically…