Error measures for DR chords: Difference between revisions
Tags: Mobile edit Mobile web edit |
→Fully DR, rooted linear: Correct analytical solution for x |
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Setting the derivative to 0 gives us the closed-form solution | Setting the derivative to 0 gives us the closed-form solution | ||
<math>x = \frac{\sum_{i=1}^n D_i }{ | <math>x = \frac{\sum_{i=1}^n D_i^2 }{\sum_{i=1}^n D_i(r_i-1)},</math> | ||
which can be plugged back into | which can be plugged back into | ||
<math>\sqrt{\sum_{ | <math>\sqrt{\sum_{i=1}^n \Bigg( 1 + \frac{D_i}{x} - r_i \Bigg)^2 }</math> | ||
to obtain the least-squares linear error. | to obtain the least-squares linear error. | ||
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== External links == | == External links == | ||
* [http:// | * [http://turbofishcrow.github.io/delta/ Inthar's DR chord explorer (includes least-squares error calculation in both domains and multiple error models)] | ||
[[Category:Math]] | [[Category:Math]] | ||