THE PADE METHOD FOR COMPUTING THE MATRIX EXPONENTIAL

We analyze the Pade method for computing the exponential of a real mat rix. More precisely, we study the roundoff error introduced by the met hod in the general case and in three special cases: (1) normal matrice s; (2) essentially nonnegative matrices (a(ij) greater than or equal t o 0, i not equal j); (3) matrices A such that A = D-1 BD, with D diago nal and B essentially nonnegative. For these special matrices, it turn s out that the Pade method is stable. Finally, we compare the Ward upp er bound with our results and show that our bounds are generally tight er.