On the bounds of approximations of holomorphic semigroups (Q1907878)

Upper bounds of variable stepsize approximations of a closed, densely defined linear operator \(A\) are derived under the restrictions that \(A\) is \(\Theta\)-sectorial (hence the semigroup \(e^{tA}\) is holomorphic) and that the approximate operator is \(A(\Theta)\)-acceptable. The results are applicable to diagonal Padé approximants.