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A process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.

*‘a basic algorithm for division’**‘Another arithmetical result presented by Brahmagupta is his algorithm for computing square roots.’**‘This first step is here reduced to a simple algorithm suitable for computer use.’**‘Mathematicians can use similar algorithms to generate fractals and other forms.’**‘Having established the nature of equilibria, Smale began to think algorithms for their computation.’**‘An algorithm known as the simplex method can be used to find these optimal strategies, but it will not be pursued here.’**‘He solved cubic equations by extending an algorithm for finding cube roots.’**‘I love numbers and always as an amusement, and more seriously than that, invented new algorithms to calculate them.’**‘Kleene's research was on the theory of algorithms and recursive functions.’**‘The appropriate degree of adjustment may be helped by nomograms or computer algorithms.’**‘One of the first applications of the simplex algorithm was to the determination of an adequate diet that was of least cost.’**‘Malcev also created a synthesis of the theory of algebras and of algorithms called constructive algebras.’**‘The theory of algorithms and a variety of computational models were developed.’**‘In fact there are many hybrid systems where asymmetric algorithms are used to distribute keys for symmetric algorithms.’**‘Leibniz considered the possibility of algorithms which would apply to logical argument as well as mathematics.’**‘All the algorithms to carry out arithmetical operations are presented in this way and no proofs are given.’**‘He began to study mathematical logic and the theory of algorithms just before 1940.’**‘The following year he wrote on number theory, making a contribution to the theory of the Euclidean algorithm.’**‘The algorithm employs quite elementary arithmetic and is stated by the authors in just 13 lines.’**‘Here there is no unfolding to a single planar component but the algorithm finds an unfolding with four planar components.’**‘The service relies on computer algorithms to select and summarise the stories generating the widest coverage.’*

Late 17th century (denoting the Arabic or decimal notation of numbers): variant (influenced by Greek arithmos ‘number’) of Middle English algorism, via Old French from medieval Latin algorismus. The Arabic source, al-Ḵwārizmī ‘the man of Ḵwārizm’ (now Khiva), was a name given to the 9th-century mathematician Abū Ja‘far Muhammad ibn Mūsa, author of widely translated works on algebra and arithmetic.

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