Retrieving "Preconditioning Techniques" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Linear Convergence

   Linked via "preconditioning techniques"

   Crucially, the asymptotic convergence factor $C$ is exactly equal to this spectral radius:
   $$C = \rho(T)$$
   Therefore, minimizing the spectral radius of the iteration matrix is equivalent to achieving the fastest possible rate of linear convergence for that specific iterative scheme. For certain high-dimensional problems involving sparse, diagonally dominant matrices, advanced preconditioning techniques aim to reduce $\rho(T)$ towards values approaching zero, effectiv…