Steepest Descent and Conjugate Gradient Methods with Variable Preconditioning

@article{Knyazev2007SteepestDA,
  title={Steepest Descent and Conjugate Gradient Methods with Variable Preconditioning},
  author={Andrew V. Knyazev and Ilya Lashuk},
  journal={SIAM J. Matrix Analysis Applications},
  year={2007},
  volume={29},
  pages={1267-1280}
}
We analyze the conjugate gradient (CG) method with variable preconditioning for solving a linear system with a real symmetric positive definite (SPD) matrix of coefficients A. We assume that the preconditioner is SPD on each step, and that the condition number of the preconditioned system matrix is bounded above by a constant independent of the step number. We show that the CG method with variable preconditioning under this assumption may not give improvement, compared to the steepest descent… CONTINUE READING
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