# A Comparative Study of Iterative Solvers Exploiting Spectral Information for SPD Systems

@article{Giraud2006ACS,
title={A Comparative Study of Iterative Solvers Exploiting Spectral Information for SPD Systems},
author={Luc Giraud and Daniel Ruiz and Ahmed Touhami},
journal={SIAM J. Sci. Comput.},
year={2006},
volume={27},
pages={1760-1786}
}
• Published 30 November 2005
• Computer Science
• SIAM J. Sci. Comput.
When solving the symmetric positive definite (SPD) linear system ${\bf A} {\bf x}^\star = {\bf b}$ with the conjugate gradient method, the smallest eigenvalues in the matrix ${\bf A}$ often slow down the convergence. Consequently if the smallest eigenvalues in ${\bf A}$ could somehow be "removed," the convergence may be improved. This observation is of importance even when a preconditioner is used, and some extra techniques might be investigated to further improve the convergence rate of the…
41 Citations

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