Abstract:
An analytic semigroup of operators on a Banach space is approximated by a sequence of positive integer powers
of a linear-fractional operator function. It is proved that the order of the approximation error in the
domain of the generating operator equals $O(n^{-2}\ln(n))$. For a self-adjoint positive definite operator $A$
decomposed into a sum of self-adjoint positive definite operators, an approximation
of the semigroup {$\exp(-tA)$} ($t\geq0$)
by weighted averages is also considered.
It is proved that the order of the approximation error in the operator norm equals $O(n^{-1/2}\ln(n))$.
Keywords:approximation of semigroup, Trotter–Chernoff formula, analytic semigroup.
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