EVALUATING MATRIX FUNCTIONS BY RESUMMATIONS ON GRAPHS: THE METHOD OF PATH-SUMS - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Matrix Analysis and Applications Année : 2013

EVALUATING MATRIX FUNCTIONS BY RESUMMATIONS ON GRAPHS: THE METHOD OF PATH-SUMS

P.-L Giscard
S. Thwaite
  • Fonction : Auteur
D. Jaksch
  • Fonction : Auteur

Résumé

We introduce the method of path-sums which is a tool for analytically evaluating a primary function of a finite square discrete matrix, based on the closed-form resummation of infinite families of terms in the corresponding Taylor series. Provided the required inverse transforms are available, our approach yields the exact result in a finite number of steps. We achieve this by combining a mapping between matrix powers and walks on a weighted directed graph with a universal graph-theoretic result on the structure of such walks. We present path-sum expressions for a matrix raised to a complex power, the matrix exponential, matrix inverse, and matrix logarithm. We present examples of the application of the path-sum method.
Fichier principal
Vignette du fichier
086288RRR.pdf (328.9 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03597518 , version 1 (04-03-2022)

Identifiants

Citer

P.-L Giscard, S. Thwaite, D. Jaksch. EVALUATING MATRIX FUNCTIONS BY RESUMMATIONS ON GRAPHS: THE METHOD OF PATH-SUMS. SIAM Journal on Matrix Analysis and Applications, 2013, 34 (2), pp.445-469. ⟨10.1137/120862880⟩. ⟨hal-03597518⟩
16 Consultations
62 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More