Abstract
AbstractThe Krylov subspace method has been investigated and refined for approximating the behaviors of finite or infinite dimensional linear operators. It has been used for approximating eigenvalues, solutions of linear equations, and operator functions acting on vectors. Recently, for time-series data analysis, much attention is being paid to the Krylov subspace method as a viable method for estimating the multiplications of a vector by an unknown linear operator referred to as a transfer operator. In this paper, we investigate a convergence analysis for Krylov subspace methods for estimating operator-vector multiplications.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Engineering
Reference45 articles.
1. Alberty, J., Carstensen, C., Funken, S.A.: Remarks around 50 lines of Matlab: short finite element implementation. Numer. Algorithms 20, 117–137 (1999)
2. Botchev, M.A., Grimm, V., Hochbruck, M.: Residual, restarting, and Richardson iteration for the matrix exponential. SIAM J. Sci. Comput. 35(3), A1376–A1397 (2013)
3. Budišić, M., Mohr, R., Mezić, I.: Applied Koopmanism. Chaos 22, 047510 (2012)
4. Črnjarić-Žic, N., Maćešić, S., Mezić, I.: Koopman operator spectrum for random dynamical systems. J. Nonlinear Sci. 20, 20 (2019)
5. Crouzeix, M., Palencia, C.: The numerical range is a $$(1+\sqrt{2})$$-spectral set. SIAM J. Matrix Anal. Appl. 38(2), 649–655 (2017)