Please use this identifier to cite or link to this item: https://doi.org/10.1137/120862880
Title: Evaluating matrix functions by resummations on graphs: The method of path-sums
Authors: Giscard, P.-L.
Thwaite, S.J.
Jaksch, D. 
Keywords: Graph theory
Matrix exponential
Matrix function
Matrix inverse
Matrix logarithm
Matrix raised to a complex power
Path
Walk
Issue Date: 2013
Citation: Giscard, P.-L., Thwaite, S.J., Jaksch, D. (2013). Evaluating matrix functions by resummations on graphs: The method of path-sums. SIAM Journal on Matrix Analysis and Applications 34 (2) : 445-469. ScholarBank@NUS Repository. https://doi.org/10.1137/120862880
Abstract: 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, the matrix inverse, and the matrix logarithm. We present examples of the application of the path-sum method. © 2013 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Matrix Analysis and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/116330
ISSN: 08954798
DOI: 10.1137/120862880
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