Approximate solution to linear regression

Problem can have 40,000 variables, most of them highly correlated.
More variables than observations in some cases. I came up with an
approach, and my question is

(1) is this an original approach?
(2) more importantly, does it always provide a fairly accurate
solution?

The problem and solution are described at http://datashaping.com/contest14004.shtml
.. The newsgroup can not render the mathematical formatting.

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