Numerical solution of the matrix equation AX + XAT+ B = 0

A recursive algorithm is shown to solve the above equation accurately for large ( n \leq 146 ), lightly damped ( \zeta \geq 10^{-3} ) systems. About 2.5n^{2} storage locations are required, and about 2.5n^{3} multiplications are performed per recursion, ten recursions being typical.