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Stability of the Peaceman-Rachford approximation. (English) Zbl 0920.47021
Let $$A$$ and $$B$$ be selfadjoint bounded from below operators in a Hilbert space. The author investigates stability of approximation (in the operator norm) of $$e^{-t(A+B)}$$ by the Peaceman-Rachford formula $p(t/2n)^n \to e^{-t(A+B)},$ where $$p(t) = (1+tA)^{-1}(1-tB)(1+tB)^{-1}(1-tA)$$.
The approximation is stable if $$\| p(t)\| \leq 1+O(t)$$. Sufficient conditions for stability are given; they involve conditions on the commutators of $$\sqrt A$$ and $$\sqrt B$$.

##### MSC:
 47B25 Linear symmetric and selfadjoint operators (unbounded)
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##### References:
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