Abstract: A substantial savings in computational time is realized by the use of plural parallel processing elements, each element having vector processing capabilities. The plurality of vector processor elements will concurrently perform calculations for a number of a groups of equations. The system determines the values of recurrent variables in a set of equations which define a linear recurrence in any order under program control by dividing said set of equations into groups of consecutive equations, determining temporary (or partial) values of the recurrence variables for each group with those recurrence variables which are derived in the equation in the next preceding group being set to zero, determining for each equation values of coefficients for those recurrence variables which were set to zero, and determining the final values of previously unsolved recurrence variables.