# A Mathematical Basis for an Interval Arithmetic Standard

Bohlender, Gerd; Kulisch, Ulrich

Serdica Journal of Computing (2010)

- Volume: 4, Issue: 1, page 29-42
- ISSN: 1312-6555

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topBohlender, 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 -

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