Error measures for DR chords: Difference between revisions
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== Conventions and introduction == | == Conventions and introduction == | ||
The idea motivating least-squares error measures on a chord as an approximation to a given delta signature is the following | The idea motivating least-squares error measures on a chord as an approximation to a given delta signature is the following: | ||
We want the error of a chord {{nowrap|1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub>}} (in increasing order, we also take {{nowrap|''r''<sub>0</sub> {{=}} 1}}), with {{nowrap|''n'' > 1}}, in the linear domain as an approximation to a | We want the error of a chord {{nowrap|1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub>}} (in increasing order, we also take {{nowrap|''r''<sub>0</sub> {{=}} 1}}), with {{nowrap|''n'' > 1}}, in the linear domain as an approximation to a delta-rational chord with signature {{nowrap|+δ<sub>1</sub> +δ<sub>2</sub> ... +δ<sub>''n''</sub>}} (possibly with some deltas free), i.e. a chord | ||
<math>x : x + \delta_1 : \cdots : x + \sum_{l=1}^n \delta_l</math> | <math>x : x + \delta_1 : \cdots : x + \sum_{l=1}^n \delta_l</math> | ||