Numerical investigations of the relative efficiency of Riccati versus non-Riccati based approaches to the determination of optimal feedback gains for linear dynamics-quadratic cost control processes over a finite interval are presented. The non-Riccati algorithms used are the so-called generalized X — Y functions [1] or Chandrasekhar-type [2] algorithms. The results of the experiments show that the generalized X — Y approach has significant computational advantages over the usual Riccati equation and, in many cases, the computational gain exceeds rough estimates based solely upon a count of the number of equations to be integrated. © 1976, IEEE.