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3.3.4 Piecewise Models

Any function tex2html_wrap_inline34165 may be cut into sections where each section fits into one class:  

math17571

A model of a function tex2html_wrap_inline34165 may be built up in pieces. To determine tex2html_wrap_inline35733 , for tex2html_wrap_inline32905 , a proper cover tex2html_wrap_inline35737 of m is found. After a proper cover tex2html_wrap_inline35737 of m is found,

math17579

Since tex2html_wrap_inline35745 , tex2html_wrap_inline34477 is concave and is simpler to evaluate than g. The union of two linear intervals is a linear interval which includes the two given intervals:

math17587

math17594

The following diagram displays the union of two linear intervals, m and n.

figure17601

As before, covers are assembled from a preferred sectioning tex2html_wrap_inline35767 , tex2html_wrap_inline35769 .


next up previous notation contents
Next: 3.3.5 Charts Up: 3.3 Linear Interval Arithmetic Previous: 3.3.3 Optimality
Jeff TupperMarch 1996