Relative distance--an error measure in round-off error analysis
Math. Comp. 39 (1982), 563-569
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Abstract: 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 , , is even more favorable, through it seems to be inferior because of two drawbacks which are not shared by relative precision: (i) the inequality is not true for . (ii) is not defined for complex . In this paper the definition of is replaced by . This definition is equivalent to the first in case , , and is free of (ii). The inequality is replaced by the more universally valid inequality . The favorable properties of are preserved in the complex case. Moreover, its definition may be generalized to linear normed spaces by . Its properties in such spaces raise the possibility that with further investigation it might become the basis for error analysis in some vector, matrix, and function spaces.
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- J. H. Wilkinson, Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, N. J., 1963. MR 0161456 (28:4661)
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