Matrix intersection problems for conditioning
|Author:||Huhtanen, Marko1; Seiskari, Otto2|
1Applied and Computational Mathematics, Faculty of Information and Electrical Engineering University of Oulu, 90570 Oulu 57, Finland
2Department of Mathematics and Systems Analysis, Aalto University Box 1100, FIN-02015, Finland
|Online Access:||PDF Full Text (PDF, 0.2 MB)|
|Persistent link:|| http://urn.fi/urn:nbn:fi-fe201902256114
Polish Academy of Sciences,Institute of Mathematics,
|Publish Date:|| 2019-02-25
Conditioning of a nonsingular matrix subspace is addressed in terms of its best conditioned elements. The problem is computationally challenging. Associating with the task an intersection problem with unitary matrices leads to a more accessible approach. A resulting matrix nearness problem can be viewed to generalize the so-called Löwdin problem in quantum chemistry. For critical points in the Frobenius norm, a differential equation on the manifold of unitary matrices is derived. Another resulting matrix nearness problem allows locating points of optimality more directly, once formulated as a problem in computational algebraic geometry.
Banach Center publications
|Pages:||195 - 210|
|Type of Publication:||
A1 Journal article – refereed
|Field of Science:||
The work of M.H. has been supported by the Academy of Finland and in part by the European
Commission project TODEQ (MTKD-CT-2005-030042). The work of O.S. has been partially supported by the Academy of Finland.
© Instytut Matematyczny PAN, 2017.