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The decomposition or approximation of a linear operator on a matrix space asa sum of Kronecker products plays an important role in matrix equations andlow-rank modeling. The approximation problem in Frobenius norm admits awell-known solution via the singular value decomposition. However, theapproximation problem in spectral norm, which is more natural for linearoperators, is much more challenging. In particular, the Frobenius norm solutioncan be far from optimal in spectral norm. We describe an alternatingoptimization method based on semidefinite programming to obtain high-qualityapproximations in spectral norm, and we present computational experiments toillustrate the advantages of our approach.

Kronecker Product Approximation of Operators in Spectral Norm via Alternating SDP