Early Papers on Interval Computations
Origins of Interval Computations: from Archimedes to 1960s
Achimedes used two-sided bounds to compute Pi:
Archimedes, "On the measurement of the
circle", In: Thomas L. Heath
(ed.), The Works of Archimedes, Cambridge University Press,
Cambridge, 1897; Dover edition, 1953, pp. 91-98.
The concept of a function having values which are bounded within
limits was discussed by W. H. Young:
W. H. Young, "Sull due funzioni a piu valori constituite dai limiti
d'una funzione di variable reale a destra ed a sinistra di ciascun
punto", Rendiconti Academia di Lincei, Classes di Scienza Fiziche,
1908, Vol. 17, No. 5, pp. 582-587.
The concept of operations with a set of multi-valued numbers was
introduced by R. C. Young, who developed a formal algebra of
The special case of closed intervals was further developed by P. S. Dwyer:
Interval mathematics was further developed by
by T. Sunaga:
and by R.
For an early history of interval computations, see also
S. Markov and K. Okumura, "The Contribution of T. Sunaga to
Interval Analysis and Reliable Computing", In: T. Csendes (ed.),
Developements in Reliable Computing, Kluwer, Dordrecht,
1999, pp. 167-188.
Selected Papers from the 1970s and 1980s
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