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 inThe Astrophysical journal Vol. 988; no. 2; pp. 158 - 163
Main Authors Yu, Bo, Liu, Wen-Hu, Yang, Xiaofeng, Zhang, Tong-Jie, Tang, Yanke
Format Journal Article
LanguageEnglish
Published Philadelphia The American Astronomical Society 01.08.2025
IOP Publishing
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ISSN0004-637X
1538-4357
1538-4357
DOI10.3847/1538-4357/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.
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
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Snippet The cosmography known as the Padé polynomials has been widely used in the reconstruction of luminosity distance, and the orders of Padé polynomials influence...
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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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