algorithm

n. (Mathematics) step-by-step procedure used to solve a problem (often includes repetition of steps); step-by-step problem-solving procedure used within software applications (Computers)

In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will proceed through a well-defined series of successive states, eventually terminating in an end-state.The concept of an algorithm originated as a means of recording procedures for solving mathematical problems such as finding the common divisor of two numbers or multiplying two numbers. A partial formalization of the concept began with attempts to solve the Entscheidungsproblem (the "decision problem") that David Hilbert posed in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" (cf Kleene 1943:274) or "effective method" (cf Rosser 1939:225); those formalizations included the Gödel-Herbrand-Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation I" of 1936, and Alan Turing's Turing machines of 1936-7 and 1939.
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Noun
1. a precise rule (or set of rules) specifying how to solve some problem
(synonym) algorithmic rule, algorithmic program
(hypernym) rule, formula
(hyponym) sorting algorithm

(n.)
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.
  

(n.)
The art of calculating by nine figures and zero.
  

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<algorithm, programming> A detailed sequence of actions to perform to accomplish some task. Named after an Iranian mathematician, Al-Khawarizmi.
Technically, an algorithm must reach a result after a finite number of steps, thus ruling out brute force search methods for certain problems, though some might claim that brute force search was also a valid (generic) algorithm. The term is also used loosely for any sequence of actions (which may or may not terminate).
Paul E. Black's Dictionary of Algorithms, Data Structures, and Problems.
(2002-02-05)