Gao, C, Zhang, X, Xu, Y et al. (5 more authors) (2018) Theoretical consideration on the convergence of the fixed-point iteration method in the CIE mesopic photometry system MES2. Optics Express, 26 (24). pp. 31351-31362. ISSN 1094-4087
Abstract
Currently the fixed-point iteration method with initial guess 0=0.5 is officially recommended by the CIE MES2 system [CIE 191:2010] in order to compute the adaptation coefficient and the mesopic luminance . However, recently, Gao et al. [Opt. Express 25, 18365 (2017)] and Shpak et al. [Lighting Res. Technol. 49, 111 (2017)] have numerically found that the fixed-point iteration method could be not convergent for large values of / . Shpak et al. suspected that, to achieve convergence, the / ratio cannot be greater than 17. In this paper, a theoretical consideration for the CIE MES2 system is given. Namely, it is shown that the ratio / be smaller than a constant 2 (≈18.1834) is a sufficient condition for the convergence of the fixed-point iteration method. In addition, a new initial guess strategy, achieving faster convergence, is proposed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement: https://www.osapublishing.org/library/license_v1.cfm#VOR-OA |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Arts, Humanities and Cultures (Leeds) > School of Design (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Dec 2018 15:18 |
Last Modified: | 10 Dec 2018 15:18 |
Status: | Published |
Publisher: | Optical Society of America (OSA) |
Identification Number: | 10.1364/OE.26.031351 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:139353 |