Relative distance—an error measure in round-off error analysis
Abraham Ziv · Mathematics of Computation · 1982
Olver ( SIAM J. Numer. Anal. , v. 15, 1978, pp. 368-393) suggested relative precision as an attractive substitute for relative error in round-off error analysis. He remarked that in certain respects the error measure d ( x ¯ , x ) = min { α | 1 − α ⩽ x / x ¯ ⩽ 1 / ( 1 − α ) } d(\bar x,x) = \min \{ \alpha |1 - \alpha \leqslant x/\bar x \leqslant 1/(1 - \alpha )\} , x ¯ ≠ 0 \bar x e 0 , x / x ¯ > 0 x/\bar x > 0 is even more favorable, through it seems to be inferior because of two drawbacks which are not shared by relative precision: (i) the inequality d ( x ¯ k , x k ) ⩽ | k | d ( x ¯ , x ) d({\bar x^k},{x^k}) \leqslant |k|d(\bar x,x) is not true fo