Shift-invert rational Krylov method for evolution equations
DOI:
https://doi.org/10.21914/anziamj.v58i0.11622Keywords:
Shift-invert rational Krylov, $\phi$-functionAbstract
In order to obtain the numerical solution of evolution equations which arise in various fields of science and technology, the computation of matrix functions called \(\phi\)-functions is required. This paper proposes a new method called the shift-invert rational Krylov method for the computation of matrix \(\phi\)-functions. This method efficiently computes the matrix \(\phi\)-functions and allows the appropriate parameters to be simply determined. References- B. Beckermann and L. Reichel, Error estimation and evaluation of matrix functions via the Faber transform. SIAM Journal on Numerical Analysis 47(5):3849–3883, 2009. doi:10.1137/080741744
- M. Crouzeix, Numerical range and functional calculus in Hilbert space. Journal of Functional Analysis 244:668–690, 2007. doi:10.1016/j.jfa.2006.10.013
- T. Gockler, Rational Krylov subspace methods for \(\phi \)-functions in exponential integrators. Karlsruher Instituts fur Technologie, 2014, Ph.D. thesis. http://d-nb.info/1060425408/34
- S. Guttel, Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection. GAMM-Mitteilungen 38(1):8–31, 2013. doi:10.1002/gamm.201310002
- Y. Hashimoto and T. Nodera, Inexact shift-invert Arnoldi method for evolution equations. ANZIAM Journal 58(E):E1–E27, 2016. doi:10.21914/anziamj.v58i0.10766
- M. Hochbruck and A. Ostermann, Exponential integrators. Acta Numerica 19:209–286, 2010. doi:10.1017/S0962492910000048
Published
2017-12-03
Issue
Section
Proceedings Computational Techniques and Applications Conference