The Collaborative International Dictionary of English v.0.48:

Algorism \Al"go*rism\, Algorithm \Al"go*rithm\, n. [OE.
   algorism, algrim, augrim, OF. algorisme, F. algorithme (cf.
   Sp. algoritmo, OSp. alguarismo, LL. algorismus), fr. the Ar.
   al-Khow[=a]rezm[imac] of Khow[=a]rezm, the modern Khiwa,
   surname of Abu Ja'far Mohammed ben Mus[=a], author of a work
   on arithmetic early in the 9th century, which was translated
   into Latin, such books bearing the name algorismus. The
   spelling with th is due to a supposed connection with Gr. ?
   number.]
   1. The art of calculating by nine figures and zero;
      computation with Arabic figures.
      [1913 Webster]

   2. the Arabic system of numeration.

   Syn: decimal system
        [WordNet 1.5]

   3. The art of calculating with any species of notation; as,
      the algorithms of fractions, proportions, surds, etc.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

algorithm \algorithm\ n.
   a precise rule (or set of rules) specifying how to solve some
   problem; a set of procedures guaranteed to find the solution
   to a problem.

   Syn: algorithmic rule, algorithmic program
        [WordNet 1.5 +PJC]

WordNet (r) 3.0 (2006):

algorithm
    n 1: a precise rule (or set of rules) specifying how to solve
         some problem [syn: algorithm, algorithmic rule,
         algorithmic program]

The Free On-line Dictionary of Computing (19 January 2023):

algorithm

    A detailed sequence of actions to
   perform to accomplish some task.  Named after the Iranian,
   Islamic mathematician, astronomer, astrologer and geographer,
   Muhammad ibn Musa al-Khwarizmi.

   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 (http://nist.gov/dads/).

   (2002-02-05)