Delta-rational chord: Difference between revisions
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</math> | </math> | ||
We use the constraint | |||
<math> | <math> 0 < \beta_1 < \beta_2 < \cdots < \beta_m </math> | ||
\ | |||
</math> | |||
and treat the DR chord as a union of fully DR chords | and treat the DR chord as a union of fully DR chords | ||
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<math> \beta_i : \beta_ir_{i,1} : \cdots : \beta_i r_{i,n_i}. </math> | <math> \beta_i : \beta_ir_{i,1} : \cdots : \beta_i r_{i,n_i}. </math> | ||
Here we require that each <math>\beta_i</math> be above the previous chord. | |||
<math> | |||
This turns the objective function into a sum of univariate objective functions | |||
<math> \displaystyle{ \sum_{k_i=1}^{n_i} \Bigg( \beta_i r_{i,k_i} - \beta_i - \sum_{{l_i}=1}^i \delta_{i,l_i} \Bigg)^2. } </math> | <math> \displaystyle{ \sum_{k_i=1}^{n_i} \Bigg( \beta_i r_{i,k_i} - \beta_i - \sum_{{l_i}=1}^i \delta_{i,l_i} \Bigg)^2. } </math> | ||