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When calculating least-squares we use the form $$Xw=y$$ This gives us an approximation, and it can happen that the resulting $w$ will be such that $Xw \lt y$ (entry-wise).

Is there a way how to make every entry in $w$ big enough so that $Xw \ge y$?

And is it possible, at the same time, to make sure every entry in $Xw$ is less that some other number?

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