Github user mengxr commented on the pull request: https://github.com/apache/spark/pull/11610#issuecomment-197199401 Locally, we are solving `A^T A x = A^T b`. In a rank deficient case, we can compute the min-length least squares solution that also minimizes `\| x \|_2`, which is unique and returned by DGELSD. This is the same as eigen decomposition because `A^T A` is symmetric. We can try that too. Ideally, we should solve the least squares problems using tall-skinny QR/SVD to get better stability. But it is a little tricky for sparse data. So I would suggest solving the normal equation locally with SVD.
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