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Next: 3.2.21 Examples with Bumpy Functions Up: 3.2 Constant Interval Arithmetic Previous: 3.2.19 Example with a Discontinuous

3.2.20 Bumpy Functions

We now consider implementing tex2html_wrap_inline35049 models. Each tex2html_wrap_inline35051 interval is given by a set of tex2html_wrap_inline35053 intervals. We previously defined the union of two tex2html_wrap_inline32653 intervals. Extending that definition results in the following method for taking the union of two tex2html_wrap_inline35053 intervals:

math14113

Another method, which uses tex2html_wrap_inline35051 to describe the result, follows:

math14131

Since each tex2html_wrap_inline35051 interval is a collection of tex2html_wrap_inline35053 intervals, the union of two tex2html_wrap_inline35051 intervals is simply the sum of the two collections:

math14141

tex2html_wrap_inline35067 . Good models of tex2html_wrap_inline32653 -bumpy functions may be built using the methods presented so far, using tex2html_wrap_inline35071 rather than tex2html_wrap_inline35073 , where appropriate.


next up previous notation contents
Next: 3.2.21 Examples with Bumpy Functions Up: 3.2 Constant Interval Arithmetic Previous: 3.2.19 Example with a Discontinuous
Jeff TupperMarch 1996