Interchangeability of the routh and jury tabular algorithms for linear system zero location

The well-known Routh and Jury tabular schemes for determination of linear system zero location relative to the left half plane and unit disc respectively are formulated as special cases of two algorithms for finding the greatest common divisor of two polynomials. Two recent extensions of the tabular methods are expressed similarly, and this enables a previously unknown 'duality' property of the two zero location algorithms to be demonstrated. Namely, that a Routh-type array can be applied to the unit disc problem, and a Jury-type array to the left half plane problem, and these applications occur in a precisely symmetrical fashion. Extensions are given for complex polynomials, and remarks are made on the problem of coefficient growth during array construcion.