A recursive algorithm for coprime fractions and Diophantine equations

The computation of coprime fractions for proper rational matrices and the solving of the minimal design problem are important in the design of multivariable systems by using polynomial fractional terms. A recursive algorithm, which fully exploits the shift-invariant property of the generalized resultants, is developed to carry out these computations. A method for solving the Diophantine equation that is based on this algorithm is outlined. This results in a significant reduction in computation as compared to the standard methods involving solution of linear algebraic equations. Some comparisons to existing methods show that the present algorithm is computationally more attractive with regard to efficiency and accuracy