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Next: 3.2.9 Examples with Piecewise Constant Up: 3.2 Constant Interval Arithmetic Previous: 3.2.7 Charts

3.2.8 Piecewise Constant Functions

We will determine tex2html_wrap_inline34159 for a constant function tex2html_wrap_inline34165 . Piecewise constant functions are handled by considering tex2html_wrap_inline34477 for tex2html_wrap_inline34475 . The procedure is remarkably similar to the procedure for globally constant functions.

We have assumed that tex2html_wrap_inline34325 . Take any tex2html_wrap_inline34327 ; a simple proof by contradiction, which follows, shows that tex2html_wrap_inline34329 is an exact bound of g:

math13022

Assume there is a point tex2html_wrap_inline34333 such that tex2html_wrap_inline34335 . Let tex2html_wrap_inline34273 , so tex2html_wrap_inline34339 :

eqnarray12325

Furthermore, tex2html_wrap_inline34251 and tex2html_wrap_inline34325 imply that tex2html_wrap_inline34229 .

figure13032

A quick review of the tex2html_wrap_inline34257 chart reveals this situation is impossible, since tex2html_wrap_inline34229 implies that tex2html_wrap_inline34301 . The tex2html_wrap_inline34257 chart predicts the sign of tex2html_wrap_inline34221 since tex2html_wrap_inline34273 .

next up previous notation contents
Next: 3.2.9 Examples with Piecewise Constant Up: 3.2 Constant Interval Arithmetic Previous: 3.2.7 Charts
Jeff TupperMarch 1996