A GENERALIZED ADI ITERATIVE METHOD

The ADI iterative method for the solution of Sylvester's equation AX - XB = C proceeds by strictly alternating between the solution of the t wo equations (A - delta(k+1)I)X2k+1 = X2k(B - delta(k+1)I) + C X2k+2(B - tau(k+1)I) = (A - tau(k+1)I)X2k+1 - C for k = 0, 1, 2,.... Here X0 is a given initial approximate solution, and the delta(k) and tau(k) a re real or complex parameters chosen so that the computed approximate solutions X(k) converge rapidly to the solution k of the Sylvester equ ation as k increases. This paper discusses the possibility of solving one of the equations in the ADI iterative method more often than the o ther one, i.e., relaxing the strict alternation requirement, in order to achieve a higher rate of convergence. Our analysis based on potenti al theory shows that this generalization of the ADI iterative method c an give faster convergence than when strict alternation is required.