3.3.23 #tex2html_wrap_inline37021# Charts

Next: 3.3.24 Examples with Binary Functions Up: 3.3 Linear Interval Arithmetic Previous: 3.3.22 Binary Functions: Two-Step Method

3.3.23 Charts

As was previously done, charts are used to graphically display the preferred sectioning of a function into concave pieces. Charts for some common binary functions follow.

The

and

charts are both identical to the

chart. The two-step method may handle charts which do not contain regions denoting that

. The given charts reveal that all of the listed binary operators may be handled directly with the two-step method, with the exception of

. Since

minimization and maximization may be handled, proceeding as follows:

The above is only a formal justification of the obvious method,

Addition, subtraction, and multiplication are particularly straightforward since each is a bilinear function. The bilinear bound is simply the function itself.

Since

the relationship, between

and

, used to aid the determination of

, for unary g, may be used to aid the determination of

, for binary g. The partial derivatives for some common binary functions follow.

math23209

Next: 3.3.24 Examples with Binary Functions Up: 3.3 Linear Interval Arithmetic Previous: 3.3.22 Binary Functions: Two-Step Method

Jeff Tupper

March 1996