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Next: 3.3.24 Examples with Binary Functions Up: 3.3 Linear Interval Arithmetic Previous: 3.3.22 Binary Functions: Two-Step Method

3.3.23 tex2html_wrap_inline35771 Charts

As was previously done, tex2html_wrap_inline35771 charts are used to graphically display the preferred sectioning of a function into concave pieces. Charts for some common binary functions follow.

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The tex2html_wrap_inline37121 and tex2html_wrap_inline37123 charts are both identical to the tex2html_wrap_inline37125 chart. The two-step method may handle charts which do not contain regions denoting that tex2html_wrap_inline37127 or tex2html_wrap_inline37129 . The given charts reveal that all of the listed binary operators may be handled directly with the two-step method, with the exception of tex2html_wrap_inline35139 . Since

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minimization and maximization may be handled, proceeding as follows:

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The above is only a formal justification of the obvious method,

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Addition, subtraction, and multiplication are particularly straightforward since each is a bilinear function. The bilinear bound is simply the function itself.

Since

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the relationship, between tex2html_wrap_inline35843 and tex2html_wrap_inline35619 , used to aid the determination of tex2html_wrap_inline35767 , for unary g, may be used to aid the determination of tex2html_wrap_inline35767 , for binary g. The partial derivatives for some common binary functions follow.

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next up previous notation contents
Next: 3.3.24 Examples with Binary Functions Up: 3.3 Linear Interval Arithmetic Previous: 3.3.22 Binary Functions: Two-Step Method
Jeff TupperMarch 1996