A generalized interval arithmetic
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.
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