@inproceedings{Pan2010RandomizedPV,
title={Randomized Preprocessing versus Pivoting II ∗},
author={Victor Y. Pan and Guoliang Qian and A. Zheng},
year={2010}
}

It is known that without pivoting Gaussian elimination can run significantly faster, particularly for matrices that have structure of Toeplitz or Hankel types, but becomes numerically unsafe. The known remedies take their toll, e.g., symmetrization squares the condition number of the input matrix. Can we fix the problem without such a punishment? Taking this challenge we combine randomized preconditioning techniques with iterative refinement and prove that this combination is expected to make… CONTINUE READING

Newton’s Iteration for Matrix Inversion, Advances and Extensions, in Matrix methods: Theory, Algorithms and Applications (dedicated to the Memory of Gene

V. Y. Pan

H. Golub, edited by Vadim Olshevsky and Eugene Tyrtyshnikov), • 2010