Error Bounds for the Krylov Subspace Methods for Computations of Matrix Exponentials

@article{Wang2017ErrorBF,
  title={Error Bounds for the Krylov Subspace Methods for Computations of Matrix Exponentials},
  author={Hao Wang and Qiang Ye},
  journal={SIAM J. Matrix Analysis Applications},
  year={2017},
  volume={38},
  pages={155-187}
}
In this paper, we present new a posteriori and a priori error bounds for the Krylov subspace methods for computing e−τAv for a given τ > 0 and v ∈ Cn, where A is a large sparse nonHermitian matrix. The a priori error bounds relate the convergence to λmin( A+A∗ 2 ), λmax( A+A∗ 2 ) (the smallest and the largest eigenvalue of the Hermitian part of A), and |λmax(A−A 2 )| (the largest eigenvalue in absolute value of the skew-Hermitian part of A), which define a rectangular region enclosing the field… CONTINUE READING

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