Preprint 21/2022

Kronecker product approximation of operators in spectral norm via alternating SDP

Mareike Dressler, André Uschmajew, and Venkat Chandrasekaran

Contact the author: Please use for correspondence this email.
Submission date: 07. Jul. 2022
Pages: 19
Download full preprint: PDF (699 kB)

The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known solution via the singular value decomposition. However, the approximation problem in spectral norm, which is more natural for linear operators, is much more challenging. In particular, the Frobenius norm solution can be far from optimal in spectral norm. We describe an alternating optimization method based on semidefinite programming to obtain high-quality approximations in spectral norm, and we present computational experiments to illustrate the advantages of our approach.

10.07.2022, 02:20