Implementation of a restarted Krylov subspace method for the evaluation of matrix functions
By M. Afanasjew, Michael C. Eiermann, Oliver G. Ernst, Stefan Güttel. 2008
108 citations recorded by the source corpus.
A new implementation of restarted Krylov subspace methods for evaluating f (A)b for a function f ,a matrix A and a vector b is proposed. In contrast to an implementation proposed previously, it requires constant work and constant storage space per restart cycle. The convergence behavior of this scheme is discussed and a new stopping criterion based on an error indicator is given. The performance of the implementation is illustrated for three parabolic initial value problems, requiring the evaluation of exp(A)b.
Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/3fb4cc35813b800d0b9c32ff0d3e0d333bc559c4
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In Computational Theory and Mathematics
In Electrical and Electronic Engineering
In Numerical Analysis
Citations in the corpus
- The Matrix Exponential (2015, unknown): “Note that a number of restarting strategies have recently been developed [1, 12, 20, 36, 43].”
- A black-box rational Arnoldi variant for Cauchy–Stieltjes matrix functions (2013, methodology): “Although restarted variants of the polynomial Arnoldi method for f(A)v have been proposed, which prevent the dimension of the Krylov space to grow above memory limit (see [20, 1, 21]), the use of finite poles ξj typically is a worthwhile alternative if linear systems with shifted versions of A can b”