An algorithm is a set of ordered logical operations that applies to a problem defined by a set of data (input data) to produce a solution (output data). An algorithm is usually written in an informal way (pseudocode) before writing it with syntax of a computer language such as C, Java, Python etc. The following is an example of a pseudocode to find \(n!\):

Algorithm you-name-it
Input: nonnegative integer \(n\)
Output: \(n!\)
\( fact=1\)
for i =2 to n
     \( fact=fact*i\)
end for
return \( fact\)

Stopping criteria: Sometimes we need a stopping criteria to terminate an algorithm. For example, when an algorithm approximates a solution \(x^*\) by constructing a sequence \(\{x_n\}\), the algorithm needs to stop after finding \(x_k\) for some \(k\). There is no universal stopping criteria as it depends on the problem, acceptable error (i.e., error \(<\) tolerance, say \(10^{-4}\) ), the maximum number of iterations etc.

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