The present manuscript describes a Riemannian-steepest-descent approach to compute the average out of a set of optical system transference matrices on the basis of a Lie-group av- eraging criterion function. The devised averaging algorithm is compared with the Harris’ exponential-mean-logarithm averaging rule, especially developed in computational oph- thalmology to compute the average character of a set of biological optical systems. Results of numerical experiments show that the iterative algorithm based on gradient steepest de- scent implemented by exponential-map stepping converges to solutions that are in good agreement with those obtained by the application of Harris’ exponential-mean-logarithm averaging rule. Such results seem to confirm that Harris’ exponential-mean-logarithm av- eraging rule is numerically optimal in a Lie-group averaging sense.

A Riemannian steepest descent approach over the inhomogeneous symplectic group: Application to the averaging of linear optical systems / Fiori, Simone. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - STAMPA. - 283:(2016), pp. 251-264. [10.1016/j.amc.2016.02.018]

A Riemannian steepest descent approach over the inhomogeneous symplectic group: Application to the averaging of linear optical systems

FIORI, Simone
2016-01-01

Abstract

The present manuscript describes a Riemannian-steepest-descent approach to compute the average out of a set of optical system transference matrices on the basis of a Lie-group av- eraging criterion function. The devised averaging algorithm is compared with the Harris’ exponential-mean-logarithm averaging rule, especially developed in computational oph- thalmology to compute the average character of a set of biological optical systems. Results of numerical experiments show that the iterative algorithm based on gradient steepest de- scent implemented by exponential-map stepping converges to solutions that are in good agreement with those obtained by the application of Harris’ exponential-mean-logarithm averaging rule. Such results seem to confirm that Harris’ exponential-mean-logarithm av- eraging rule is numerically optimal in a Lie-group averaging sense.
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/238959
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