In the paper, http://people.duke.edu/~hpgavin/ce281/lm.pdf, equations 1), 2), and 3) refer to the chi-squared error criterion.

Equation 2) is reproduced below.

$$ \chi^2({\mathbf p}) = (\mathbf y- \hat{\mathbf y}({\mathbf p}))^{\mathsf T}{\mathbf W}(\mathbf y- \hat{\mathbf y}({\mathbf p})) $$

What does the superscript T notation represent? Equation 2) appears to be short hand notation for equation 1), which sums over i from 1 to m.

I dusting off my old paper (and code) on the Marquardt algorithm from 1966 as well as learning the updates, like Levenberg-Marquardt, that have been made since.

I am not and never was a math major.

  • 4
    $\begingroup$ Transpose: en.wikipedia.org/wiki/Transpose ... $y$ is supposed to be a column vector, $y^{\mathrm{T}}$ simply denotes its transpose to a row vector so that the inner products can be denoted simply products of matrices (where a column vector is a matrix with one column and a row vector a matrix with one row). $\endgroup$ Oct 3 '13 at 22:47
  • $\begingroup$ Thanks. Should put this comment be in an answer, no? $\endgroup$
    – KeithSmith
    Oct 3 '13 at 22:55

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