BibTeX
@MISC{Pan_randomizedmatrix,
author = {Victor Y. Pan and Guoliang Qian and Ai-long Zheng},
title = {Randomized Matrix Computations III ∗},
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
It is well known that random matrices tend to be well conditioned, and we employ this property to advance some fundamental matrix computations. We prove effectiveness of our novel techniques of randomized preconditioning, estimate the condition numbers of random Toeplitz and circulant matrices, numerically stabilize Gaussian elimination with no pivoting and block Gaussian elimination, compute 2 × 2 matrix factorization where both diagonal blocks are better conditioned than an ill conditioned input matrix, and apply our dual variation of the Sherman–Morrison–Woodbury formula to low-rank matrix approximation. Our formal study and numerical tests show significant progress versus the known algorithms and should motivate further research efforts.
Keyphrases
matrix computation iii sherman morrison woodbury formula formal study input matrix significant progress fundamental matrix computation random matrix randomized preconditioning research effort block gaussian elimination novel technique diagonal block gaussian elimination random toeplitz numerical test condition number dual variation circulant matrix low-rank matrix approximation matrix factorization
