The effect of non-optimal bases on the convergence of Krylov subspace methods

@article{Simoncini2005TheEO,
  title={The effect of non-optimal bases on the convergence of Krylov subspace methods},
  author={Valeria Simoncini and Daniel B. Szyld},
  journal={Numerische Mathematik},
  year={2005},
  volume={100},
  pages={711-733}
}
There are many examples where non-orthogonality of a basis for Krylov subspace methods arises naturally. These methods usually require less storage or computational effort per iteration than methods using an orthonormal basis (optimal methods), but the convergence may be delayed. Truncated Krylov subspace methods and other examples of non-optimal methods have been shown to converge in many situations, often with small delay, but not in others. We explore the question of what is the effect of… CONTINUE READING