Rank-3 scale theorems: Difference between revisions
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* Say ''S'' is ''pointwise-least-squares-LQ'' if the sum of (R(k) - L(k))^2 over k ∈ {0, ..., n} is minimized for *all* modes of ''S''. | * Say ''S'' is ''pointwise-least-squares-LQ'' if the sum of (R(k) - L(k))^2 over k ∈ {0, ..., n} is minimized for *all* modes of ''S''. | ||
* Say ''S'' is ''pointwise-minimax-LQ'' if the max distance max{|R(k)-L(k)| : k} is minimized for *all* modes of ''S''. | * Say ''S'' is ''pointwise-minimax-LQ'' if the max distance max{|R(k)-L(k)| : k} is minimized for *all* modes of ''S''. | ||
* | * Assume ''S'' is a 2-step scale. Then ''S'' is ''slope-LQ'' if the slope between any two pair of points (representing a ''k''-mosstep) is one of the two nearest possible slopes (in the set {k/0,...,0/k}) to b/a. | ||
* Say that ''S'' is ''floor-LQ'' if some mode of ''S'' gives the graph of floor(b/a*x). | |||
===== MV2 is equivalent to LQ in 2-step scales (WIP) ===== | ===== MV2 is equivalent to LQ in 2-step scales (WIP) ===== | ||