Product Formulas and Error Estimates
S. T. Kuroda, Kazuhiro Kurata · Birkhäuser Basel eBooks · 1995
Recently there has been considerable interest in the use of Trotter type product formulas, in theoretical physics (see [15] and literature cited there) as well as in numerical computation (see, e.g., [6] and the literature cited there). The basic formula is the Trotter product formula e A+B = lim n→∞ (e A/n e B/n ) n , which is a two-factor product formula. It is also widely recognized that the symmetrized three factor formula e A+B = lim n→∞ (e A/2n e B/n e A/2n ) n is effective in numerical computations. In fact the order of error formally derived from the Taylor expansion is O(n -1) and O(n -2), respectively. We also mention that a systematic investigation for constructing multi-factor product formulas with higher order of error has been done by M. Suzuki ([14], [15]) (for bounded generators). The convergence of multi-factor formulas as the number of factors becomes large is also proved in [15]. (For numerical applications of multi-factor formulas, see also [5].)