Combination of Jacobi-Davidson and conjugate gradients for the partial symmetric eigenproblem

@article{Notay2002CombinationOJ,
  title={Combination of Jacobi-Davidson and conjugate gradients for the partial symmetric eigenproblem},
  author={Yvan Notay},
  journal={Numerical Lin. Alg. with Applic.},
  year={2002},
  volume={9},
  pages={21-44}
}
To compute the smallest eigenvalues and associated eigenvectors of a real symmetric matrix, we consider the Jacobi–Davidson method with inner preconditioned conjugate gradient iterations for the arising linear systems. We show that the coe9cient matrix of these systems is indeed positive de:nite with the smallest eigenvalue bounded away from zero. We also establish a relation between the residual norm reduction in these inner linear systems and the convergence of the outer process towards the… CONTINUE READING
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