A generalized interval arithmetic

  • E. R. Hansen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 29)


We have introduced and illustrated a generalized interval analysis which reduces the inherent lack of sharpness of o.i.a. to a second order effect. Our method may not be useful if second order quantities are not truly negligible. Moreover, our method is of little value if the original data for a problem is real rather than intervals of non-zero width.

However, it is substantially better than o.i.a. for many problems. Moreover, it provides a more powerful tool in some cases such as in bounding multiple roots.

The rules for multiplication and division should be regarded as tentative. Further study may reveal that alternative rules are preferable.

As a final comment, we note that it is easily shown that g.i.a. is subdistributive.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ramon E. Moore, "Interval Analysis", Prentice-Hall, 1966.Google Scholar
  2. [2]
    Eldon R. Hansen, "On Solving Systems of Equations Using Interval Arithmetic", Math. Comp., 22(1968), 374–384.Google Scholar
  3. [3]
    R. H. Dargel, F. R. Loscalzo, and T. H. Witt, "Automatic Error Bounds on Real Zeros of Rational Functions", Comm. ACM, 9(1966), 806–809.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • E. R. Hansen
    • 1
  1. 1.Lockheed Palo Alto Research LaboratoryPalo AltoUSA

Personalised recommendations