Please use this identifier to cite or link to this item:
|Title:||Evaluating matrix functions by resummations on graphs: The method of path-sums|
Matrix raised to a complex power
|Source:||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|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Feb 15, 2018
WEB OF SCIENCETM
checked on Jan 30, 2018
checked on Feb 19, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.