کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6419812 1631772 2016 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A Riemannian steepest descent approach over the inhomogeneous symplectic group: Application to the averaging of linear optical systems
ترجمه فارسی عنوان
یک رویکرد تدریجی رومیان بر روی گروه سمپلکتیک غیرواقعی: کاربرد در میانگین سیستمهای نوری خطی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 283, 20 June 2016, Pages 251-264
نویسندگان
,