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.
B. Aggarwal and James
W. Burgmeier, A round-off error model with applications to
arithmetic expressions, SIAM J. Comput. 8 (1979),
no. 1, 60–72. MR 522970
A. N. Kolmogorov & S. C. Fomin, Elements of the Theory of Functions and Functional Analysis, Graylock Press, Rochester, New York, 1957.
W. J. Olver, A new approach to error arithmetic, SIAM J.
Numer. Anal. 15 (1978), no. 2, 368–393. MR 0483379
H. Sterbenz, Floating-point computation, Prentice-Hall, Inc.,
Englewood Cliffs, N.J., 1974. Prentice-Hall Series in Automatic
0349062 (50 #1556)
W. Stewart, Introduction to matrix computations, Academic
Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New
York-London, 1973. Computer Science and Applied Mathematics. MR 0458818
H. Wilkinson, Rounding errors in algebraic processes,
Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
- Vijay B. Aggarwal & James W. Burgmeier, "A roundoff error model with applications to arithmetic expressions," SIAM J. Comput., v. 8, 1979, pp. 60-72. MR 522970 (81b:68031)
- A. N. Kolmogorov & S. C. Fomin, Elements of the Theory of Functions and Functional Analysis, Graylock Press, Rochester, New York, 1957.
- F. W. J. Olver, "A new approach to error arithmetic," SIAM J. Numer. Anal., v. 15, 1978, pp. 368-393. MR 0483379 (58:3385)
- Pat H. Sterbenz, Floating Point Computation, Prentice-Hall, Englewood Cliffs, N. J., 1974. MR 0349062 (50:1556)
- G. W. Stewart, Introduction to Matrix Computations, Academic Press, New York and London, 1973. MR 0458818 (56:17018)
- J. H. Wilkinson, Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, N. J., 1963. MR 0161456 (28:4661)
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