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> This iteration seems to be for "iteratively reweighted least squares" not
>for backfitting. And lm.wfit may solve multiple linear equation using
>QR decomposition; but I am not sure.

   Let me tell you something about my guess above.
The iteration below is from 1 to maxit.

  for (iter in 1:maxit) {
        ------
        fit <- eval(bf.call)
        ------
  }

The help of "gam.control()" says:
   maxit: maximum number of local scoring iterations
   bf.maxit: maximum number of backfitting iterations

Therefore the iteration above is local scoring iteration not
backfitting iteration.

   The first line of "lm.wfit()" is:
function (x, y, w, offset = NULL, method = "qr", tol = 1e-07,
 singular.ok = TRUE, ...)
There is no "bf.maxit" or its equivalent in these arguments. And it
contains 'method = "qr"'; it may mean that this routine solves
a multiple linear equation using QR decomposition.
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