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Given a matrix $A$ of size $k \times k$ over real numbers. The goal is to compute the nuclear norm (see this) of the matrix.

One way is to use SVD (singular value decomposition) and then calculate the trace of the diagonal matrix obtained in the SVD decomposition. Thus, the proposed method's runtime complexity will be $O(k^3)$.

Is there any faster way to compute the nuclear norm of the matrix?

asked Jan 1 at 14:36
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    $\begingroup$ The algorithm described by you is best $\endgroup$ Commented Jan 2 at 3:50

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