A Mathematical Basis for an Interval Arithmetic Standard

Bohlender, Gerd, and Kulisch, Ulrich. "A Mathematical Basis for an Interval Arithmetic Standard." Serdica Journal of Computing 4.1 (2010): 29-42. <http://eudml.org/doc/11373>.

@article{Bohlender2010,
abstract = {Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied in section 7. The desirability of variable length interval arithmetic is also discussed in the paper. The requirement to adapt the digital computer to the needs of interval arithmetic is as old as interval arithmetic. An obvious, simple possible solution is shown in section 8.},
author = {Bohlender, Gerd, Kulisch, Ulrich},
journal = {Serdica Journal of Computing},
keywords = {Interval Arithmetic; IEEE Standardization; Variable Precision Interval Arithmetic; Evaluation of Functions; Hardware Support; interval arithmetic; IEEE standardization; variable precision interval arithmetic; evaluation of functions; hardware support},
language = {eng},
number = {1},
pages = {29-42},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {A Mathematical Basis for an Interval Arithmetic Standard},
url = {http://eudml.org/doc/11373},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Bohlender, Gerd
AU - Kulisch, Ulrich
TI - A Mathematical Basis for an Interval Arithmetic Standard
JO - Serdica Journal of Computing
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 4
IS - 1
SP - 29
EP - 42
AB - Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied in section 7. The desirability of variable length interval arithmetic is also discussed in the paper. The requirement to adapt the digital computer to the needs of interval arithmetic is as old as interval arithmetic. An obvious, simple possible solution is shown in section 8.
LA - eng
KW - Interval Arithmetic; IEEE Standardization; Variable Precision Interval Arithmetic; Evaluation of Functions; Hardware Support; interval arithmetic; IEEE standardization; variable precision interval arithmetic; evaluation of functions; hardware support
UR - http://eudml.org/doc/11373
ER -