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Next: 3.3.6 Monotonic Sections Up: 3.3 Linear Interval Arithmetic Previous: 3.3.4 Piecewise Models

3.3.5 tex2html_wrap_inline35771 Charts

Some examples of tex2html_wrap_inline35767 follow.

math17786

A tex2html_wrap_inline35767 chart is used to visualize the sections the function g is cut into. Here are tex2html_wrap_inline35771 charts for the preceding examples:

figure17827

The tex2html_wrap_inline35833 and tex2html_wrap_inline35835 charts are both identical to the tex2html_wrap_inline35837 chart.

Determination of tex2html_wrap_inline35767 , for twice differentiable g, is aided by the relationship between tex2html_wrap_inline35843 and tex2html_wrap_inline35619 : if tex2html_wrap_inline35847 and tex2html_wrap_inline34561 , then

math18054

As an example, consider tex2html_wrap_inline34565 , tex2html_wrap_inline33647 ; since

math18061

for tex2html_wrap_inline35859 , which implies tex2html_wrap_inline34573 , the following holds:

math18066

From the aforementioned relationship between tex2html_wrap_inline35843 and tex2html_wrap_inline35619 , it follows that tex2html_wrap_inline35869 , for any tex2html_wrap_inline35871 ; so tex2html_wrap_inline35873 .

next up previous notation contents
Next: 3.3.6 Monotonic Sections Up: 3.3 Linear Interval Arithmetic Previous: 3.3.4 Piecewise Models
Jeff TupperMarch 1996