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Relevant bibliographies by topics / Euclidean algorithm

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Academic literature on the topic 'Euclidean algorithm'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Euclidean algorithm"

1

Okazaki, Hiroyuki, Yosiki Aoki, and Yasunari Shidama. "Extended Euclidean Algorithm and CRT Algorithm." Formalized Mathematics 20, no. 2 (2012): 175–79. http://dx.doi.org/10.2478/v10037-012-0020-2.

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Summary In this article we formalize some number theoretical algorithms, Euclidean Algorithm and Extended Euclidean Algorithm [9]. Besides the a gcd b, Extended Euclidean Algorithm can calculate a pair of two integers (x, y) that holds ax + by = a gcd b. In addition, we formalize an algorithm that can compute a solution of the Chinese remainder theorem by using Extended Euclidean Algorithm. Our aim is to support the implementation of number theoretic tools. Our formalization of those algorithms is based on the source code of the NZMATH, a number theory oriented calculation system developed by

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Gilman, Jane. "The non-Euclidean Euclidean algorithm." Advances in Mathematics 250 (January 2014): 227–41. http://dx.doi.org/10.1016/j.aim.2013.09.012.

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Balkhair, Eynas. "Euclidean Algorithm Analysis." International Journal of Engineering Research and Applications 14, no. 12 (2024): 32–37. https://doi.org/10.9790/9622-14123237.

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Okazaki, Hiroyuki, Koh-ichi Nagao, and Yuichi Futa. "Maximum Number of Steps Taken by Modular Exponentiation and Euclidean Algorithm." Formalized Mathematics 27, no. 1 (2019): 87–91. http://dx.doi.org/10.2478/forma-2019-0009.

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Summary In this article we formalize in Mizar [1], [2] the maximum number of steps taken by some number theoretical algorithms, “right–to–left binary algorithm” for modular exponentiation and “Euclidean algorithm” [5]. For any natural numbers a, b, n, “right–to–left binary algorithm” can calculate the natural number, see (Def. 2), AlgoBPow(a, n, m) := ab mod n and for any integers a, b, “Euclidean algorithm” can calculate the non negative integer gcd(a, b). We have not formalized computational complexity of algorithms yet, though we had already formalize the “Euclidean algorithm” in [7]. For “

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Afghani, Said Al, and Widhera Yoza Mahana Putra. "Clustering with Euclidean Distance, Manhattan - Distance, Mahalanobis - Euclidean Distance, and Chebyshev Distance with Their Accuracy." Indonesian Journal of Statistics and Its Applications 5, no. 2 (2021): 369–76. http://dx.doi.org/10.29244/ijsa.v5i2p369-376.

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There are several algorithms to solve many problems in grouping data. Grouping data is also known as clusterization, clustering takes advantage to solve some problems especially in business. In this note, we will modify the clustering algorithm based on distance principle which background of K-means algorithm (Euclidean distance). Manhattan, Mahalanobis-Euclidean, and Chebyshev distance will be used to modify the K-means algorithm. We compare the clustered result related to their accuracy, we got Mahalanobis - Euclidean distance gives the best accuracy on our experiment data, and some results

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Bras-Amorós, Maria, and Michael E. O’Sullivan. "The Symmetric Key Equation for Reed–Solomon Codes and a New Perspective on the Berlekamp–Massey Algorithm." Symmetry 11, no. 11 (2019): 1357. http://dx.doi.org/10.3390/sym11111357.

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This paper presents a new way to view the key equation for decoding Reed–Solomon codes that unites the two algorithms used in solving it—the Berlekamp–Massey algorithm and the Euclidean algorithm. A new key equation for Reed–Solomon codes is derived for simultaneous errors and erasures decoding using the symmetry between polynomials and their reciprocals as well as the symmetries between dual and primal codes. The new key equation is simpler since it involves only degree bounds rather than modular computations. We show how to solve it using the Euclidean algorithm. We then show that by reorgan

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MIERNOWSKI, TOMASZ, and ARNALDO NOGUEIRA. "Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transformations." Ergodic Theory and Dynamical Systems 33, no. 1 (2011): 221–46. http://dx.doi.org/10.1017/s014338571100085x.

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AbstractThe two-dimensional homogeneous Euclidean algorithm is the central motivation for the definition of the classical multidimensional continued fraction algorithms, such as Jacobi–Perron, Poincaré, Brun and Selmer algorithms. The Rauzy induction, a generalization of the Euclidean algorithm, is a key tool in the study of interval exchange transformations. Both maps are known to be dissipative and ergodic with respect to Lebesgue measure. Here we prove that they are exact.

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RUZSA, IMRE Z., and PETER P. VARJU. "Euclidean algorithm in different norms." Publicationes Mathematicae Debrecen 78, no. 1 (2011): 245–49. http://dx.doi.org/10.5486/pmd.2011.4804.

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Gorokhovskyi, Semen, and Artem Laiko. "Euclidean Algorithm for Sound Generation." NaUKMA Research Papers. Computer Science 4 (December 10, 2021): 48–51. http://dx.doi.org/10.18523/2617-3808.2021.4.48-51.

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Euclidean algorithm is known by humanity for more than two thousand years. During this period many applications for it were found, covering different disciplines and music is one of those. Such algorithm application in music first appeared in 2005 when researchers found a correlation between world music rhythm and the Euclidean algorithm result, defining Euclidean rhythms as the concept.In the modern world, music could be created using many approaches. The first one being the simple analogue, the analogue signal is just a sound wave that emitted due to vibration of a certain medium, the one th

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Van Den Dries, Lou, and Yiannis N. Moschovakis. "Is the Euclidean Algorithm Optimal Among its Peers?" Bulletin of Symbolic Logic 10, no. 3 (2004): 390–418. http://dx.doi.org/10.2178/bsl/1102022663.

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The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem(a, b) is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from (relative to) the remainder function rem, meaning that in computing its time complexity function cε (a, b), we assume that the values rem(x, y) are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch more is known about cε(a, b), but this simple-to-prove upper bound suggests the proper formulation of the Eu

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Dissertations / Theses on the topic "Euclidean algorithm"

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Hirata, Tomio. "VLSI Algorithm for Euclidean Distance Transform." INTELLIGENT MEDIA INTEGRATION NAGOYA UNIVERSITY / COE, 2004. http://hdl.handle.net/2237/10354.

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SILVA, Alecio Soares. "Um Estudo Sobre Aplicação do Algoritmo de Euclides." Universidade Federal de Campina Grande, 2014. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/2160.

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Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-11-09T17:51:39Z No. of bitstreams: 1 ALECIO SOARES SILVA – DISSERTAÇÃO (PPGMat) 2014.pdf: 873139 bytes, checksum: 9a35db2563d66eb36f4dabfe6e5cd45e (MD5)<br>Made available in DSpace on 2018-11-09T17:51:39Z (GMT). No. of bitstreams: 1 ALECIO SOARES SILVA – DISSERTAÇÃO (PPGMat) 2014.pdf: 873139 bytes, checksum: 9a35db2563d66eb36f4dabfe6e5cd45e (MD5) Previous issue date: 2014-08<br>Capes<br>Neste trabalho consideramos o uso de algoritmo de Euclides com o intuito de aplicá-lo de uma forma interdisciplinar. Para atingir este

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Clark, David Alan. "The Euclidean algorithm for Galois extensions of the rational numbers." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=39408.

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Let K be a totally real, quartic, Galois extension of $ doubq$ whose ring of integers R is a principal ideal domain. If there is a prime ideal p of R such that the unit group maps onto $(R/{ bf p} sp2$)*, then R is a Euclidean domain. This criterion is generalized to arbitrary Galois extensions.<br>Let E be an elliptic curve over a number field F. Suppose ($F: doubq rbrack le 4$ and $F(E lbrack q rbrack ) not subseteq F$ for all primes q such that F contains a primitive $q sp{ rm th}$ root of unity, then the reduced elliptic curve $ tilde{E}(F sb{ bf p})$ is cyclic infinitely often. In general

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高木, 直史, and Naofumi Takagi. "A VLSI algorithm for computing the Euclidean norm of a 3D vector." IEEE, 2000. http://hdl.handle.net/2237/5291.

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Zegeye, Wondimu K., and Seifemichael B. Amsalu. "Minimum Euclidean Distance Algorithm for Indoor WiFi Received Signal Strength (RSS) Fingerprinting." International Foundation for Telemetering, 2016. http://hdl.handle.net/10150/624190.

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While WiFi-based indoor localization is attractive, the need for a significant degree of pre-deployment effort is a key challenge. In this paper, indoor localization with no pre-deployment effort in an indoor space, such as an office building corridor, with WiFi coverage but no apriori knowledge of the placement of the access points(APs) is implemented for mobile devices. WiFi Received Signal Strength(RSS) in the considered environment is used to build radio maps using WiFi fingerprinting approach. Two architectures are developed based on this localization algorithm. The first one involve

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Crook, Deborah. "Polynomial invariants of the Euclidean group action on multiple screws : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Master of Science in Mathematics /." ResearchArchive@Victoria e-Thesis, 2009. http://hdl.handle.net/10063/1205.

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Hilmar, Jan. "Intersection of algebraic plane curves : some results on the (monic) integer transfinite diameter." Thesis, University of Edinburgh, 2008. http://hdl.handle.net/1842/3843.

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Part I discusses the problem of determining the set of intersection points, with corresponding multiplicities, of two algebraic plane curves. We derive an algorithm based on the Euclidean Algorithm for polynomials and show how to use it to find the intersection points of two given curves. We also show that an easy proof of Bézout’s Theorem follows. We then discuss how, for curves with rational coefficients, this algorithm can bemodified to find the intersection points with coordinates expressed in terms of algebraic extensions of the rational numbers. Part II deals with the problem of determi

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Smith, Andrea Marie. "A dual algorithm for the weighted Euclidean distance min-max location problem in R² and R³." Connect to this title online, 2009. http://etd.lib.clemson.edu/documents/1246559571/.

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Franco, Felipe Barbosa. "O jogo dominó algébrico." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8622.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2018-06-29T10:56:16Z No. of bitstreams: 2 Dissertação - Felipe Barbosa Franco - 2018.pdf: 2597060 bytes, checksum: b4c3ff56766b29c5a01cd7de1c3ba60a (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-06-29T11:55:57Z (GMT) No. of bitstreams: 2 Dissertação - Felipe Barbosa Franco - 2018.pdf: 2597060 bytes, checksum: b4c3ff56766b29c5a01cd7de1c3ba60a (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Made ava

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Ranjitkar, Hari Sagar, and Sudip Karki. "Comparison of A*, Euclidean and Manhattan distance using Influence map in MS. Pac-Man." Thesis, Blekinge Tekniska Högskola, Institutionen för datalogi och datorsystemteknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-11800.

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Context An influence map and potential fields are used for finding path in domain of Robotics and Gaming in AI. Various distance measures can be used to find influence maps and potential fields. However, these distance measures have not been compared yet. ObjectivesIn this paper, we have proposed a new algorithm suitable to find an optimal point in parameters space from random parameter spaces. Finally, comparisons are made among three popular distance measures to find the most efficient. Methodology For our RQ1 and RQ2, we have implemented a mix of qualitative and quantitative approach and fo

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Books on the topic "Euclidean algorithm"

1

Haddad, Gidget. Euclidean symmetries in mathematics. White Word Publications, 2012.

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Schaake, A. G. Generalizing Euclid's algorithm, via the regular and Moebius knot trees, order-n arithmetics. Waikato Polytechnic, 1990.

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Li, Yuying. A Newton acceleration of the Weiszfeld algorithm for minimizing the sum of Euclidean distances. Cornell Theory Center, Cornell University, 1995.

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Bultheel, Adhemar. Linear algebra, rational approximation, and orthogonal polynomials. Elsevier, 1997.

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Ghandehari, Mostafa. Minkowski's inequality for convex curves. University of Texas at Arlington, Dept. of Mathematics, 2001.

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Reinhard, Klette, ed. Euclidean shortest paths: Exact or approximate algorithms. Springer-Verlag, 2011.

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Tovey, Craig A. Some foundations for empirical study in the Euclidean spatial model of social choice. Naval Postgraduate School, 1991.

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8

Florian, Luca, ed. Analytic number theory: Exploring the anatomy of integers. American Mathematical Society, 2012.

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Bochnerriesz Means On Euclidean Spaces. World Scientific Publishing Co Pte Ltd, 2013.

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Introduction to Theory of Optimization in Euclidean Space. Taylor & Francis Group, 2019.

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Book chapters on the topic "Euclidean algorithm"

1

Sunar, Berk. "Euclidean Algorithm." In Encyclopedia of Cryptography and Security. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_27.

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Sunar, Berk. "Euclidean Algorithm." In Encyclopedia of Cryptography, Security and Privacy. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-030-71522-9_27.

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Eisenbrand, Friedrich. "The Euclidean Algorithm." In Algorithms Unplugged. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-15328-0_12.

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Forman, Sylvia, and Agnes M. Rash. "The Euclidean Algorithm." In The Whole Truth About Whole Numbers. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11035-6_5.

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Stillwell, John. "The Euclidean algorithm." In Undergraduate Texts in Mathematics. Springer New York, 2003. http://dx.doi.org/10.1007/978-0-387-21735-2_2.

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Boito, Paola. "The Euclidean algorithm." In Structured Matrix Based Methods for Approximate Polynomial GCD. Edizioni della Normale, 2011. http://dx.doi.org/10.1007/978-88-7642-381-9_3.

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Sunar, Berk. "Binary Euclidean Algorithm." In Encyclopedia of Cryptography and Security. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_25.

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Karloff, Howard. "The Euclidean Algorithm." In Compact Textbooks in Mathematics. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-33203-6_2.

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Sunar, Berk. "Binary Euclidean Algorithm." In Encyclopedia of Cryptography, Security and Privacy. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-030-71522-9_25.

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Camion, P. "An Iterative Euclidean Algorithm." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51082-6_72.

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Conference papers on the topic "Euclidean algorithm"

1

Cao, Shuxian, Jingrong Chen, and Jiaojiao Gou. "Binary Particle Swarm Optimization Algorithm for Euclidean Steiner Tree." In 2024 4th International Conference on Computer Science and Blockchain (CCSB). IEEE, 2024. http://dx.doi.org/10.1109/ccsb63463.2024.10735644.

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Zhang, Zhen, Niansong Zhang, and Aimin Wang. "Improved Euclidean Clustering and Segmentation Algorithm for Workpiece Identification." In 2024 IEEE International Conference on Mechatronics and Automation (ICMA). IEEE, 2024. http://dx.doi.org/10.1109/icma61710.2024.10633002.

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Chen, Chao, Zhongfeng Wang, Yunghsiang S. Han, and Baoming Bai. "Reformulated Euclidean Algorithm and Optimized (OREA) Architecture for Reed-Solomon Decoding." In 2024 International Symposium on Information Theory and Its Applications (ISITA). IEEE, 2024. https://doi.org/10.23919/isita60732.2024.10858228.

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Gao, Donglin, Honglei Qin, and Fuhe Li. "Research on the Comprehensive Performance Evaluation Method of Genetic Algorithm Based on Euclidean Distance Minimization." In 2024 8th International Workshop on Control Engineering and Advanced Algorithms (IWCEAA). IEEE, 2024. https://doi.org/10.1109/iwceaa63616.2024.10823848.

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Tyrtyshnikov, E. E., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Euclidean Algorithm and Hankel Matrices." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790129.

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Pottier, Loïc. "The Euclidean algorithm in dimension n." In the 1996 international symposium. ACM Press, 1996. http://dx.doi.org/10.1145/236869.236894.

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Pan, Victor Y., and Xinmao Wang. "Acceleration of Euclidean algorithm and extensions." In the 2002 international symposium. ACM Press, 2002. http://dx.doi.org/10.1145/780506.780533.

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Cohen, Liron, Tansel Uras, Shiva Jahangiri, Aliyah Arunasalam, Sven Koenig, and T. K. Satish Kumar. "The FastMap Algorithm for Shortest Path Computations." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/198.

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We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph. Later, at runtime, a shortest path between any two nodes can be computed with an A* search using the Euclidean distances as heuristic. Our preprocessing algorithm, called FastMap, is inspired by the data-mining algorithm of the same name and runs in near-linear time. Hence, FastMap is orders of magnitude faster than competing appr

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Chen, Shuang, Junli Li, and Xiuying Wang. "A Fast Exact Euclidean Distance Transform Algorithm." In Graphics (ICIG). IEEE, 2011. http://dx.doi.org/10.1109/icig.2011.34.

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Sorenson, Jonathan. "An analysis of Lehmer's Euclidean GCD algorithm." In the 1995 international symposium. ACM Press, 1995. http://dx.doi.org/10.1145/220346.220378.

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Reports on the topic "Euclidean algorithm"

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Casey, Stephen D., and Brian M. Sadler. Modifications of the Euclidean Algorithm for Isolating Periodicities from a Sparse Set of Noisy Measurements. Defense Technical Information Center, 1995. http://dx.doi.org/10.21236/ada455379.

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