2007 International Symposium on Nonlinear Theory and its Applications
Inversion of extremely ill-conditioned matrices using a faithfully rounded dot product
Siegfried M. Rump,
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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.