Does least squares regularization have to be iterative?

SirTristan
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Does a http://en.wikipedia.org/wiki/Tikhonov_regularization" solution for least squares have to be iteratively solved? Or is there a way to perform regularization via linear algebra, the way linear regression can be done by solving the (XTX)B=XTy normal equations?
 
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Anyone know if this needs to be iteratively accomplished?
 
Might there be someone who has a definitive answer to this issue? On whether regularization can be algebraically solved or not.
 

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