کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6419812 | 1631772 | 2016 | 14 صفحه PDF | دانلود رایگان |
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 averaging criterion function. The devised averaging algorithm is compared with the Harris' exponential-mean-logarithm averaging rule, especially developed in computational ophthalmology 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 descent 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 averaging rule is numerically optimal in a Lie-group averaging sense.
Journal: Applied Mathematics and Computation - Volume 283, 20 June 2016, Pages 251-264