Optimization: Difference between revisions

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The Euclidean norm aka ''L''2 norm resembles real-world distances.

The ~~Minkowskian norm,~~ Manhattan norm or taxicab norm aka ''L''1 norm resembles movement of taxicabs in Manhattan – it can only traverse horizontally or vertically. A diagonal movement mounts to two steps.

The Manhattan norm or taxicab norm aka ''L''1 norm resembles movement of taxicabs in Manhattan – it can only traverse horizontally or vertically. A diagonal movement mounts to two steps.

The Chebyshevian norm aka ''L''infinity norm is the opposite of the Minkowskian norm – it is the maximum number of steps in any direction, so a diagonal movement is the same as a horizontal or vertical one.

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|+Table of common tunings

|-

! Weight-skew\Order !! Chebyshevian (''L''1 tuning) !! Euclidean (''L''2 tuning) !! ~~Minkowskian~~ (''L''infinity tuning)

! Weight-skew\Order !! Chebyshevian (''L''1 tuning) !! Euclidean (''L''2 tuning) !! Manhattan (''L''infinity tuning)

|-

| Tenney Tenney-Weil || || [[TE tuning]] [[TWE tuning]] || [[TOP tuning]]

|-

| ~~Frobenius~~ ~~Frobenius~~-Weil || || [[Frobenius tuning]] ~~FWE~~ tuning ||

| Equilateral Equilateral-Weil || || [[Frobenius tuning]] EWE tuning ||

|-

| Benedetti Benedetti-Weil || || [[BE tuning]] BWE tuning || [[BOP tuning]]

@@ Line 34: / Line 34: @@
 The Euclidean norm aka ''L''<sup>2</sup> norm resembles real-world distances.
-The Minkowskian norm, Manhattan norm or taxicab norm aka ''L''<sup>1</sup> norm resembles movement of taxicabs in Manhattan – it can only traverse horizontally or vertically. A diagonal movement mounts to two steps.
+The Manhattan norm or taxicab norm aka ''L''<sup>1</sup> norm resembles movement of taxicabs in Manhattan – it can only traverse horizontally or vertically. A diagonal movement mounts to two steps.
 The Chebyshevian norm aka ''L''<sup>infinity</sup> norm is the opposite of the Minkowskian norm – it is the maximum number of steps in any direction, so a diagonal movement is the same as a horizontal or vertical one.
@@ Line 75: / Line 75: @@
 |+Table of common tunings
 |-
-! Weight-skew\Order !! Chebyshevian<br>(''L''<sup>1</sup> tuning) !! Euclidean<br>(''L''<sup>2</sup> tuning) !! Minkowskian<br>(''L''<sup>infinity</sup> tuning)
+! Weight-skew\Order !! Chebyshevian<br>(''L''<sup>1</sup> tuning) !! Euclidean<br>(''L''<sup>2</sup> tuning) !! Manhattan<br>(''L''<sup>infinity</sup> tuning)
 |-
 | Tenney<br>Tenney-Weil || || [[TE tuning]]<br>[[TWE tuning]] || [[TOP tuning]]<br>
 |-
-| Frobenius<br>Frobenius-Weil || || [[Frobenius tuning]]<br>FWE tuning ||
+| Equilateral<br>Equilateral-Weil || || [[Frobenius tuning]]<br>EWE tuning ||
 |-
 | Benedetti<br>Benedetti-Weil || || [[BE tuning]]<br>BWE tuning || [[BOP tuning]]<br>