Verified computation for the matrix Lambert W function

Miyajima, Shinya

doi:10.1016/j.amc.2019.06.069

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Range Of κ Increasing/decreasing Table Note1

Introduction1

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Cited by 4 publications

(2 citation statements)

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“…If b(0) ≥ 0, then we see that b(θ) > 0 for any θ ∈ I 0 , which implies r ± (θ) < 0 for any θ ∈ I D . If b(0) < 0, then there exists a unique 0 < ϕ < ϕ * such that b(ϕ) = 0, and we have D(0) < 0 by (18). Hence, D(θ) have a unique maximal point D(ϕ * ) > 0 at θ = ϕ * and a unique minimal point D(ϕ) < 0 at θ = ϕ.…”

Section: Range Of κ Increasing/decreasing Table Notementioning

confidence: 96%

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Stieltjes Transforms and R-Transforms Associated with Two-Parameter Lambert–Tsallis Functions

Nakashima

Graczyk

2023

Entropy

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In this paper, we study a two-parameter family of Stieltjes transformations related to holomorphic Lambert–Tsallis functions, which are a two-parameter generalization of the Lambert function. Such Stieltjes transformations appear in the study of eigenvalue distributions of random matrices associated with some growing statistically sparse models. A necessary and sufficient condition on the parameters is given for the corresponding functions being Stieltjes transformations of probabilistic measures. We also give an explicit formula of the corresponding R-transformations.

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Section: Range Of κ Increasing/decreasing Table Notementioning

confidence: 96%

“…In Mezö and Baricz [ 14 ], z before

is replaced by rational function of z (see also [ 15 , 16 ]) and in da Silva and Ramos [ 11 ],

is replaced by the Tsallis q -exponential function. The matrix Lambert W function is considered in [ 17 , 18 ].…”

Section: Introductionmentioning

confidence: 99%