Kronecker Product Approximation of Operators in Spectral Norm via Alternating SDP
Event details
| Date | 09.02.2023 |
| Hour | 11:00 › 12:00 |
| Speaker | Prof. André Uschmajew - University of Augsburg |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Computational Mathematics Seminar
Abstract : 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. Based on joint work with Mareike Dressler and Venkat Chandrasekaran.
Abstract : 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. Based on joint work with Mareike Dressler and Venkat Chandrasekaran.
Practical information
- General public
- Free
Organizer
- Prof. Daniel Kessner
Contact
- Prof. Daniel Kressner
Samantha Bettschen