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Standard Wilkinson-type error estimates of floating-point algorithms involve a factor $$\gamma _k:=k\mathbf {u}/(1-k\mathbf {u})$$ γ k : = k u / ( 1 - k u ) for $$\mathbf {u}$$ u denoting the relative rounding error unit of a floating-point number system. Recently, it was shown that, for many standard algorithms such as matrix multiplication, LU- or Cholesky decomposition,...
The result of a floating-point operation is usually defined to be the floating-point number nearest to the exact real result together with a tie-breaking rule. This is called the first standard model of floating-point arithmetic, and the analysis of numerical algorithms is often solely based on that. In addition, a second standard model is used specifying the maximum relative error with respect to...
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