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https://issues.apache.org/jira/browse/MATH-1094?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13882277#comment-13882277
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Luc Maisonobe commented on MATH-1094:
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I think the behaviour is correct.
The getSolver method for QR decomposition provides a solver for A X = B in the
least squares sense.
This means the X comuted by the solver is minimizes || A X - B ||, it does not
find 0, only a minumum norm.
In your case, the system is rectangular, so there is no way a true solution can
be achieved.
I have verified (using simple loops and gnuplot countour plots) that indeed the
x = 7.5, y = 5.5 does minimizes the norm, which is 39.0.
> Incorrect linear system solution
> --------------------------------
>
> Key: MATH-1094
> URL: https://issues.apache.org/jira/browse/MATH-1094
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.2
> Environment: Oracle JDK7
> Linux x86-64
> Reporter: Bogdan Bezpartochnyy
> Labels: patch
> Attachments: Main.java
>
>
> Firstly I would like to point out that I'm not very proficient in linear
> algebra, but in my opinion the following behavior should not occur. When I
> solve the following linear system by hand it has no solution, but in commons
> math using QRDecomposition it outputs x1= 7.5 x2 = 5.5
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