Average condition number for solving linear equations

Abstract

We study an average condition number and an average loss of precision for the solution of linear equations and prove that the average case is strongly related to the worst case. This holds if the perturbations of the matrix are measured in Frobenius or spectral norm or componentwise. In particular, for the Frobenius norm we show that one gains about log2n+0.9 bits on the average as compared to the worst case, n being the dimension of the system of linear equations. © 1986.