Variable Accuracy of Matrix-Vector Products in Projection Methods for Eigencomputation

@article{Simoncini2005VariableAO,
  title={Variable Accuracy of Matrix-Vector Products in Projection Methods for Eigencomputation},
  author={Valeria Simoncini},
  journal={SIAM J. Numerical Analysis},
  year={2005},
  volume={43},
  pages={1155-1174}
}
We analyze the behavior of projection-type schemes, such as the Arnoldi and Lanczos methods, for the approximation of a few eigenvalues and eigenvectors of a matrix A, when A cannot be applied exactly but only with a possibly large perturbation. This occurs for instance in shiftand-invert procedures or when dealing with large generalized eigenvalue problems. We theoretically show that the accuracy with which A is applied at each iteration can be relaxed, as convergence to specific eigenpairs… CONTINUE READING
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Inexact Rayleigh quotient-type methods for eigenvalue computations

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