Delta-rational chord: Difference between revisions
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which can be plugged back into the error formula to obtain the error. (We multiply the 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> chord by x in order to compare it to the target DR chord on the same isodifferential series.) | which can be plugged back into the error formula to obtain the error. (We multiply the 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> chord by x in order to compare it to the target DR chord on the same isodifferential series.) | ||
This error measure is called '''naive least-squares error'''. Least-squares delta error does not depend on whether the chord whose error is being measured is 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> or the same chord linearly shifted to have root x. Unfortunately, this error measure does not form a metric on the set of delta signatures with a fixed number of terms. | This error measure is called '''naive least-squares error''' (NLS error). Least-squares delta error does not depend on whether the chord whose error is being measured is 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> or the same chord linearly shifted to have root x. Unfortunately, this error measure does not form a metric on the set of delta signatures with a fixed number of terms. | ||
This error measure was found by Inthar and groundfault. | This error measure was found by Inthar and groundfault. | ||
==== Symmetric least-squares error ==== | ==== Symmetric least-squares error ==== | ||
'''Symmetric least-squares error''' is found by solving | '''Symmetric least-squares error''' (SLS error) is found by solving | ||
<math> | <math> | ||