The present work shows that Harris' exponential-mean-log averaging rule over the space of optical transference matrices may be regarded as an instance of the Kolmogoroff-Nagumo averaging rule over the affine symplectic group. As such, Harris' averaging rule may be generalized to a phi-mean-phi^{-1} rule that can be implemented by different phi maps. The present work also shows that the involved maps may be computed in closed form by low-degree polynomial expressions.
Kolmogoroff-Nagumo mean over the affine symplectic group of matrices / Fiori, Simone. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - STAMPA. - 266:(2015), pp. 820-837. [10.1016/j.amc.2015.05.063]
Kolmogoroff-Nagumo mean over the affine symplectic group of matrices
FIORI, Simone
2015-01-01
Abstract
The present work shows that Harris' exponential-mean-log averaging rule over the space of optical transference matrices may be regarded as an instance of the Kolmogoroff-Nagumo averaging rule over the affine symplectic group. As such, Harris' averaging rule may be generalized to a phi-mean-phi^{-1} rule that can be implemented by different phi maps. The present work also shows that the involved maps may be computed in closed form by low-degree polynomial expressions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.