Delta-rational chord: Difference between revisions
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=== Symmetric least-squares error === | === Symmetric least-squares error === | ||
With the same assumptions as above (D<sub>1</sub>, ..., D<sub>n</sub> and E<sub>1</sub>, ..., E<sub>n</sub> two lists of ''cumulative'' deltas), the '''symmetric least-squares error''' (SLS error) is found by solving both | With the same assumptions as above (D<sub>1</sub>, ..., D<sub>n</sub> and E<sub>1</sub>, ..., E<sub>n</sub> two lists of ''cumulative'' deltas), and also requiring the target delta signature to be written for 1:1+δ<sub>1</sub>:..., the '''symmetric least-squares error''' (SLS error) is found by solving both | ||
<math> | <math> | ||
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since the Hessian of this function at the minimum is positive definite. | since the Hessian of this function at the minimum is positive definite. | ||
It satisfies SLSE({D_i}, {E_i}) = SLSE({E_i}, {D_i}). | It satisfies SLSE({D_i}, {E_i}) = SLSE({E_i}, {D_i}). However, it is invariant under scaling neither of the arguments. | ||
=== Open problems === | === Open problems === | ||