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Next: 3.2.8 Piecewise Constant Functions Up: 3.2 Constant Interval Arithmetic Previous: 3.2.6 Piecewise Models

3.2.7 tex2html_wrap_inline34501 Charts

Some examples of tex2html_wrap_inline34489 follow.

math12549

A tex2html_wrap_inline34489 chart is used to visualize the sections the function g is cut into. Here are tex2html_wrap_inline34501 charts for the preceding examples:

figure12572

Determination of tex2html_wrap_inline34489 , for differentiable g, is aided by the relationship between tex2html_wrap_inline34555 and tex2html_wrap_inline34221 : if tex2html_wrap_inline34559 and tex2html_wrap_inline34561 , then

math13000

As an example, consider tex2html_wrap_inline34565 , tex2html_wrap_inline34567 ; since

math13006

for tex2html_wrap_inline34571 , which implies tex2html_wrap_inline34573 , the following holds:

math13010

From the aforementioned relationship between tex2html_wrap_inline34555 and tex2html_wrap_inline34221 , it follows that tex2html_wrap_inline34581 , for any tex2html_wrap_inline34583 ; so tex2html_wrap_inline34585 .

next up previous notation contents
Next: 3.2.8 Piecewise Constant Functions Up: 3.2 Constant Interval Arithmetic Previous: 3.2.6 Piecewise Models
Jeff TupperMarch 1996