Early Papers on Interval Computations

Origins of Interval Computations: from Archimedes to 1960s

Achimedes used two-sided bounds to compute Pi: The concept of a function having values which are bounded within limits was discussed by W. H. Young: For positive quantities, rules for the arithmetic of intervals were explicitly stated and applied to evaluation of rational expressions by Vladimir M. Bradis*: The concept of operations with a set of multi-valued numbers was introduced by R. C. Young, who developed a formal algebra of multi-valued numbers: The special case of closed intervals (not necessarily positive) was further developed by P. S. Dwyer: Interval mathematics was further developed by M. Warmus: by T. Sunaga: and by R. E. Moore

For an early history of interval computations, see also

Selected Papers from the 1970s and 1980s


*This approach was further developed in several other publications of V. M. Bradis:

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