What are some of the best methods for solving a Dense Rank Deficient Linear System $Ax = b$, where $A$ is Dense, Symmetric but possibly Rank Deficient. I know SVD can solve it pretty nicely while constraining the solution to be unit which is actually fine for me. But I am wondering if there is a faster method than this. I heard GMRES can do good job for Sparse system, how about Dense systems?
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In what sense "rank deficient"? Does it come from an ill-posed problem? Have you tried pivoted QR decomposition? Is it consistent? – Algebraic Pavel Feb 18 '15 at 21:57
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Here you can find a good selection of methods for ill-posed problems. – Algebraic Pavel Feb 18 '15 at 21:58