Abstract
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].)
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© 1995 Birkhäuser Verlag Basel/Switzerland
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Kuroda, S.T., Kurata, K. (1995). Product Formulas and Error Estimates. In: Demuth, M., Schulze, BW. (eds) Partial Differential Operators and Mathematical Physics. Operator Theory Advances and Applications, vol 78. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9092-2_23
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DOI: https://doi.org/10.1007/978-3-0348-9092-2_23
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