Smoothed Analysis for the Conjugate Gradient Algorithm
arXiv:1605.06438 · doi:10.3842/SIGMA.2016.109
Abstract
The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix. We estimate all finite moments of a natural halting time when the random perturbation is drawn from the Laguerre unitary ensemble in a critical scaling regime explored in Deift et al. (2016). These estimates are used to analyze the expected iteration count in the framework of smoothed analysis, introduced by Spielman and Teng (2001). The rigorous results are compared with numerical calculations in several cases of interest.
References in corpus (6)
- Level-Spacing Distributions and the Airy Kernel
- Smoothed analysis of algorithms
- Universality in Numerical Computations with Random Data. Case Studies
- How long does it take to compute the eigenvalues of a random symmetric matrix?
- Universality for the Toda algorithm to compute the largest eigenvalue of a random matrix
- On the condition number of the critically-scaled Laguerre Unitary Ensemble