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Matrix intersection problems for conditioning

Volume 112 / 2017

Marko Huhtanen, Otto Seiskari Banach Center Publications 112 (2017), 195-210 MSC: 15A12, 65F35. DOI: 10.4064/bc112-0-11


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.


  • Marko HuhtanenApplied and Computational Mathematics
    Faculty of Information and Electrical Engineering
    University of Oulu
    90570 Oulu 57, Finland
  • Otto SeiskariDepartment of Mathematics and Systems Analysis
    Aalto University
    Box 1100
    FIN-02015, Finland

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