A priori worst-case error bounds for floating-point computations

Author

Krämer, Walter

Author_Institution

Inst. fur Wissenschaftliches Rechnen und Math. Modellbildung, Karlsruhe Univ., Germany

fYear

1997

fDate

6-9 Jul 1997

Firstpage

64

Lastpage

71

Abstract

A new technique for the a-priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in this paper, combined with interval arithmetic, lead to the implementation of reliable software routines which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function exp(x)-1 that has been published by Tang (1992) is analyzed using these new tools. The result shows the high quality of the new approach

Keywords

error analysis; floating point arithmetic; function evaluation; software reliability; subroutines; table lookup; a-priori worst-case error bounds; exponential function; floating-point computations; interval arithmetic; reliable software routines; table-lookup algorithm; Algorithm design and analysis; Computer errors; Digital arithmetic; Equations; Error analysis; Floating-point arithmetic; Linear systems; Reliability theory;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Arithmetic, 1997. Proceedings., 13th IEEE Symposium on

Conference_Location

Asilomar, CA

ISSN

1063-6889

Print_ISBN

0-8186-7846-1

Type

conf

DOI

10.1109/ARITH.1997.614880

Filename

614880