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On Sinkhorn's DAD theorem and the self-consistency equation in COSMO-based activity coefficient models
Citation Link: https://doi.org/10.15480/882.15987
Publikationstyp
Journal Article
Date Issued
2025-10-10
Sprache
English
Author(s)
TORE-DOI
Journal
Volume
73
Issue
17
Start Page
3791
End Page
3808
Citation
Linear and multilinear algebra 73 (17): 3791â3808 (2025)
Publisher DOI
Scopus ID
Publisher
Taylor & Francis
In a 1966 paper, Sinkhorn proved that for any real square matrix A which has only positive entries there exists a uniquely determined real diagonal matrix D with positive diagonal entries such that đ”:=DAD is stochastic, i.e. all row sums of B are equal to 1. Moreover, Sinkhorn stated an iterative method for computing D. Nowadays, Sinkhorn's result and its variants are often referred to as DAD theorems. The purpose of this article is twofold. On the one hand, we give the link between Sinkhorn's DAD theorem and the self-consistency equation in COSMO-based activity coefficient models in chemical engineering. On the other hand, we give a new constructive proof of Sinkhorn's DAD theorem by using classical fixed-point theory. Hereby, the larger class of nonnegative matrices with positive diagonal is considered. Our proof uniformly provides convergence for a number of iterative methods for computing D. Some of them are used in practice although, to the best of our knowledge, a formal proof of convergence is missing.
Subjects
Sinkhornâs DAD theorem
positive matrices
stochastic matrices
COSMO-RS
COSMO-SAC
self-consistency equation
statistical thermodynamics
DDC Class
510: Mathematics
Publication version
publishedVersion
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On Sinkhorn s DAD theorem and the self-consistency equation in COSMO-based activity coefficient models.pdf
Type
Main Article
Size
1.75 MB
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