INTERVAL_ARITHMETIC
swMATH ID:  4681 
Software Authors:  Kearfott, R.Baker 
Description:  Algorithm 763: INTERVAL  ARITHMETIC: A Fortran 90 module for an interval data type Interval arithmetic is useful in automatically verified computations, that is, in computations in which the algorithm itself rigorously proves that the answer must lie within certain bounds. In addition to rigor, interval arithmetic also provides a simple and sometimes sharp method of bounding ranges of functions for global optimization and other tasks. Convenient use of interval arithmetic requires an interval data type in the programming language. Although various packages supply such a data type, previous ones are machine specific, obsolete, and unsupported, for languages other than Fortran, or commercial. The Fortran 90 module INTERVAL  ARITHMETIC provides a portable interval data type in Fortran 90. This data type is based on two doubleprecision real Fortran storage units. Module INTERVAL  ARITHMETIC uses the Fortran 77 library INTLIB (ACM TOMS Algorithm 737) as a supporting library. The module has been employed extensively in the author’s own research 
Homepage:  http://dl.acm.org/citation.cfm?id=235815.235816 
Programming Languages:  Fortran 90 
Keywords:  interval arithmetic; Fortran 90 module \( ext {INTERVAL}sb  ext {ARITHMETIC}\); computer arithmetic; error analysis; operator overloading; portability; automatically verified computations 
Related Software:  INTLIB; INTOPT_90; GSL; EISPACK; Matlab; LAPACK; GlobSol; Python; Algorithm 719; Algorithm 818; Algorithm 694; Algorithm 722; knitr; RStudio; Algorithm 695; Hadoop; Rcpp; PVM; LINPACK; PSBLAS 
Referenced in:  9 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Algorithm 763: INTERVAL\(_ \)ARITHMETIC: A Fortran 90 module for an interval data type. Zbl 0884.65041 Kearfott, R. Baker 
1996

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Referenced by 8 Authors
4  Kearfott, Baker 
2  Gentle, James E. 
1  Chachuat, Benoît 
1  Dian, Jianwei 
1  Flores, Juan J. 
1  Kinoshita, Takehiko 
1  Latifi, M. A. 
1  Nakao, Mitsuhiro T. 
Referenced in 5 Serials
2  ACM Transactions on Mathematical Software 
2  Springer Texts in Statistics 
1  Journal of Computational and Applied Mathematics 
1  Journal of Complexity 
1  Optimization Methods & Software 
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