University of Oulu

Huhtanen, M. & Seiskari, O. (2017). Matrix intersection problems for conditioning. In Banach Center Publications (pp. 195-210). doi: 10.4064/bc112-0-11

Matrix intersection problems for conditioning

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Author: Huhtanen, Marko1; Seiskari, Otto2
Organizations: 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
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.2 MB)
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Language: English
Published: Polish Academy of Sciences, Institute of Mathematics, 2017
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.

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Series: Banach Center publications
ISSN: 0137-6934
ISSN-E: 1730-6299
ISSN-L: 0137-6934
Volume: 112
Pages: 195 - 210
DOI: 10.4064/bc112-0-11
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: 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.
Copyright information: © Instytut Matematyczny PAN, 2017.