Relative distance--an error measure in round-off error analysis

Author:
Abraham Ziv

Journal:
Math. Comp. **39** (1982), 563-569

MSC:
Primary 65G05

DOI:
https://doi.org/10.1090/S0025-5718-1982-0669649-2

MathSciNet review:
669649

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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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0669649-2

Keywords:
Relative error,
round-off error analysis,
metric

Article copyright:
© Copyright 1982
American Mathematical Society