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Scalability of k-Tridiagonal Matrix Singular Value Decomposition

Singular value decomposition has recently seen a great theoretical improvement for k-tridiagonal matrices, obtaining a considerable speed up over all previous implementations, but at the cost of not ordering the singular values. We provide here a refinement of this method, proving that reordering singular values does not affect performance. We complement our refinement with a scalability study on a real physical cluster setup, offering surprising results. Thus, this method provides a major step up over standard industry implementations.