Summary
2007 International Symposium on Nonlinear Theory and its Applications
2007
Session Number:18AM1-E
Session:
Number:18AM1-E-1
Inversion of extremely ill-conditioned matrices using a faithfully rounded dot product
Siegfried M. Rump,
pp.168-171
Publication Date:2007/9/16
Online ISSN:2188-5079
DOI:10.34385/proc.41.18AM1-E-1
Summary:
Recently the author together with Shin’ichi Oishi and Takeshi Ogita developed an algorithm to compute a faithful rounding of dot products. The algorithm allows to computed a faithfully rounded result with K-fold accuracy as well. We show that this suffices to approximate the inverse of arbitrarily ill-conditioned matrices in double precision. No higher precision is used, only the precise dot product.