Conditioning and Padé Approximation of the Logarithm of a Matrix

Conditioning and Padé Approximation of the Logarithm of a Matrix

In this work we (i) use the theory of piecewise analytic functions to represent the Frechet derivative of any primary matrix function, in particular of primary logarithms; (ii) propose an indicator to assess inherent difficulties to compute a logarithm; and (iii) revisit Pade approximation technique...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:SIAM journal on matrix analysis and applications 2000, Vol.21 (3), p.913-930
Hauptverfasser: Dieci, Luca, Papini, Alessandra
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Eigenvalues
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In this work we (i) use the theory of piecewise analytic functions to represent the Frechet derivative of any primary matrix function, in particular of primary logarithms; (ii) propose an indicator to assess inherent difficulties to compute a logarithm; and (iii) revisit Pade approximation techniques for the principal logarithm of block triangular matrices.
ISSN:0895-4798
1095-7162
DOI:10.1137/S089547989834531X