A theoretical analysis is proposed, aimed at investigating the character of those power series expansions recently considered for the evaluation of several types of diffraction catastrophes. A hyperlinear convergence is found to be the signature for such expansions, so that the results of the numerical experiments recently carried out find a meaningful interpretation in terms of the accelerating action operated by the Weniger transformation. As an important by-product of our analysis, simple criteria, aimed at numerically optimizing the diffraction catastrophe evaluations, are provided through analytical expressions. (C) 2011 Optical Society of America
Borghi, R. (2011). Optimizing diffraction catastrophe evaluation. OPTICS LETTERS, 36(22), 4413-4415 [10.1364/OL.36.004413].
Optimizing diffraction catastrophe evaluation
BORGHI, Riccardo
2011-01-01
Abstract
A theoretical analysis is proposed, aimed at investigating the character of those power series expansions recently considered for the evaluation of several types of diffraction catastrophes. A hyperlinear convergence is found to be the signature for such expansions, so that the results of the numerical experiments recently carried out find a meaningful interpretation in terms of the accelerating action operated by the Weniger transformation. As an important by-product of our analysis, simple criteria, aimed at numerically optimizing the diffraction catastrophe evaluations, are provided through analytical expressions. (C) 2011 Optical Society of AmericaI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
