Stability Analysis of the Two-level Orthogonal Arnoldi Procedure

@article{Lu2016StabilityAO,
  title={Stability Analysis of the Two-level Orthogonal Arnoldi Procedure},
  author={Ding Lu and Yangfeng Su and Zhaojun Bai},
  journal={SIAM J. Matrix Analysis Applications},
  year={2016},
  volume={37},
  pages={195-214}
}
The second-order Arnoldi (SOAR) procedure is an algorithm for computing an orthonormal basis of the second-order Krylov subspace. It has found applications in solving quadratic eigenvalue problems and model order reduction of second-order dynamical systems among others. Unfortunately, the SOAR procedure can be numerically unstable. The two-level orthogonal Arnoldi (TOAR) procedure has been proposed as an alternative of SOAR to cure the numerical instability. In this paper, we provide a rigorous… CONTINUE READING