Publications in Scientific Journals:

T. Jawecki:
"A study of defect-based error estimates for the Krylov approximation of phi-functions";
Numerical Algorithms, 1 (2021).

English abstract:
Prior recent work, devoted to the study of polynomial Krylov techniques for the approximation of the action of the matrix exponential exp(tA)v, is extended to the case of associated phi-functions (which occur within the class of exponential integrators). In particular, a posteriori error bounds and estimates, based on the notion of the defect (residual) of the Krylov approximation are considered. Computable error bounds and estimates are discussed and analyzed. This includes a new error bound which favorably compares to existing error bounds in specific cases. The accuracy of various error bounds is characterized in relation to corresponding Ritz values of A. Ritz values yield properties of the spectrum of A (specific properties are known a priori, e.g., for Hermitian or skew-Hermitian matrices) in relation to the actual starting vector v and can be computed. This gives theoretical results together with criteria to quantify the achieved accuracy on the fly. For other existing error estimates, the reliability and performance are studied by similar techniques. Effects of finite precision (floating point arithmetic) are also taken into account.

matrix exponential, phi-functions, Krylov approximation, upper bound, a posteriori error estimation

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.