Talk:Least squares

Justifying derivation of general solution for linear least squares

I think the notation $Y$ here is a little confusing, because $Y$ makes it seem like it could be a matrix, when in fact it has to be a vector:

$L(D,{\vec {\beta }})=||X{\vec {\beta }}-Y||^{2}=(X{\vec {\beta }}-Y)^{T}(X{\vec {\beta }}-Y)=Y^{T}Y-Y^{T}X{\vec {\beta }}-{\vec {\beta }}^{T}X^{T}Y+{\vec {\beta }}^{T}X^{T}X{\vec {\beta }}$

I'd consider replacing $Y$ with ${\vec {y}}$. — Preceding unsigned comment added by Fadmmatt (talk • contribs) 17:53, 26 July 2020 (UTC)

Nonlinear least squares: notation

In the equation immediately under the paragraph that begins "The Jacobian J is a function of...", the meaning of k changes silently in the middle of the equation, which is horribly confusing to someone less than completely comfortable with the topic. If you know what's going on, then you realize that the superscript k used early in the equation refers to the iteration, but the subscript k in the summation later in that equation is an index over the parameter number. If you aren't so confident, then you wonder why you suddenly are summing over iteration numbers. The confusion is aggravated in the immediately following paragraph and equation, where the text reads

(...) solved for $\Delta \beta _{j}$:

but $\Delta \beta _{j}$ does not actually appear in the accompanying equation; it is only implied by the unindexed subscript j in that equation, and k again is (silently) used in the new sense, as the summation index over parameter number.

I think the easiest solution would be either to change all the k superscript indices referring to iteration to some other symbol, e.g. a capital K, as this would distinguish notationally between the two meanings and retain the use of subscript k as a summation index, OR to insert the word superscript into the first paragraph of this section to indicate that only superscripts refer to iteration numbers. I think that latter is closest to standard usage, so I've made that change. BSVulturis (talk) 19:22, 11 April 2017 (UTC)

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