The Optimal Padé Polynomial for Reconstruction of Luminosity Distance Based on 10-fold Cross Validation
The cosmography known as the Padé polynomials has been widely used in the reconstruction of luminosity distance, and the orders of Padé polynomials influence the reconstructed result derived from Padé approximation. In this paper, we present a more general scheme of selecting optimal Padé polynomial...
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| Published in | The Astrophysical journal Vol. 988; no. 2; pp. 158 - 163 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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01.08.2025
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| ISSN | 0004-637X 1538-4357 1538-4357 |
| DOI | 10.3847/1538-4357/adeb81 |
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| Abstract | The cosmography known as the Padé polynomials has been widely used in the reconstruction of luminosity distance, and the orders of Padé polynomials influence the reconstructed result derived from Padé approximation. In this paper, we present a more general scheme of selecting optimal Padé polynomial for reconstruction of luminosity distance based on 10-fold cross validation. Then the proposed scheme is applied to Pantheon+ data set. The numerical results clearly indicate that the proposed procedure has a remarkable ability to distinguish Padé approximations with different orders for the reconstruction of the luminosity distance. We conclude that the (2,1) Padé approximation is the optimal approach that can well explain Pantheon+ data at low and high redshifts. Future applications of this scheme could help choose the optimal model that is more suitable for cosmological observation data at hand and gain a deeper understanding of the Universe. |
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| AbstractList | The cosmography known as the Padé polynomials has been widely used in the reconstruction of luminosity distance, and the orders of Padé polynomials influence the reconstructed result derived from Padé approximation. In this paper, we present a more general scheme of selecting optimal Padé polynomial for reconstruction of luminosity distance based on 10-fold cross validation. Then the proposed scheme is applied to Pantheon+ data set. The numerical results clearly indicate that the proposed procedure has a remarkable ability to distinguish Padé approximations with different orders for the reconstruction of the luminosity distance. We conclude that the (2,1) Padé approximation is the optimal approach that can well explain Pantheon+ data at low and high redshifts. Future applications of this scheme could help choose the optimal model that is more suitable for cosmological observation data at hand and gain a deeper understanding of the Universe. |
| Author | Zhang, Tong-Jie Yu, Bo Yang, Xiaofeng Liu, Wen-Hu Tang, Yanke |
| Author_xml | – sequence: 1 givenname: Bo orcidid: 0000-0002-9849-1762 surname: Yu fullname: Yu, Bo organization: Beijing Normal University School of Physics and Astronomy, Beijing 100875, tjzhang@bnu.edu.cn People’s Republic of China – sequence: 2 givenname: Wen-Hu surname: Liu fullname: Liu, Wen-Hu organization: Dezhou University School of Mathematics and Big Data, Dezhou 253023, People’s Republic of China – sequence: 3 givenname: Xiaofeng orcidid: 0000-0002-1265-5747 surname: Yang fullname: Yang, Xiaofeng organization: Xinjiang Key Laboratory of Radio Astrophysics , Urumqi 830011, People’s Republic of China – sequence: 4 givenname: Tong-Jie orcidid: 0000-0002-3363-9965 surname: Zhang fullname: Zhang, Tong-Jie organization: Beijing Normal University Institute for Frontiers in Astronomy and Astrophysics, Beijing 102206, People’s Republic of China – sequence: 5 givenname: Yanke orcidid: 0000-0003-4207-1694 surname: Tang fullname: Tang, Yanke organization: Dezhou University College of Physics and Electronic Information, Dezhou 253023, People’s Republic of China |
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| SubjectTerms | Akaike information criterion Bayesian information criterion Cross-validation Luminosity Observational cosmology Pade approximation Polynomials Reconstruction |
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| Title | The Optimal Padé Polynomial for Reconstruction of Luminosity Distance Based on 10-fold Cross Validation |
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