Reciprocal averaging is a widely used algorithm for correspondence analysis. The correspondence analysis itself is sometimes also called reciprocal averaging.
The initial data set is a two-way contingency table, representing the frequency of particular combinations of values of two categorical variables. The algorithm is iterative – it starts from assigning arbitrary numerical scores to one variable values, say, to rows of the table, and, after series of iterations the procedure converges to a stable assignment of scores to values of both variables. Then, the next sets of scores may be derived in the same way, taking care about orthogonality (zero correlation) of the new sets of scores to the previous ones.