Delta-rational chord: Difference between revisions

Inthar (talk | contribs)
Inthar (talk | contribs)
Line 74: Line 74:
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''' (NLS error). NLS 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). This error measure does not form a metric on the set of delta signatures with a fixed number of terms, since it is not symmetric.


This error measure was found by Inthar and groundfault.
This error measure was found by Inthar and groundfault.