Rational approximations of semigroups without scaling and squaring
Discrete and Continuous Dynamical Systems- Series A
We show that for all q ≥ 1 and 1 ≤ i ≤ q there exist pairwise conjugate complex numbers bq;i and q;i with Re(q;i) > 0 such that for any generator (A;D(A)) of a bounded, strongly continuous semigroup T(t) on Banach space X with resolvent R(A) := (I A)-1 the expression bq;1 t R( q;1 t ;A) + bq;2 t R( q;2 t ;A) + + bq;q t R( q;q t ;A) provides an excellent approximation of the semigroup T(t) on D(A2q-1). Precise error estimates as well as applications to the numerical inversion of the Laplace transform are given.
Neubrander, F., Ozer, K., & Sandmaier, T. (2013). Rational approximations of semigroups without scaling and squaring. Discrete and Continuous Dynamical Systems- Series A, 33 (11-12), 5305-5317. https://doi.org/10.3934/dcds.2013.33.5305