Journal ArticleDOI
Combinatorics of Higher Derivatives of Inverses
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(2002).Abstract:
(2002). Combinatorics of Higher Derivatives of Inverses. The American Mathematical Monthly: Vol. 109, No. 3, pp. 273-277.read more
Citations
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Journal ArticleDOI
Taylor expansion of the inverse function with application to the Langevin function
TL;DR: In this paper, a simple recurrence procedure for calculating Taylor series coefficients of the inverse function is proposed, which can be used to express an inverse function especially if it is given in an implicit form.
Journal ArticleDOI
Uniform estimates for bilinear Hilbert transforms and bilinear maximal functions associated to polynomials
Xiaochun Li,Lechao Xiao +1 more
TL;DR: In this paper, the authors studied the bilinear Hilbert transforms and maximal functions associated to non-flat polynomial curves and obtained uniform estimates of the lower bound of the upper bound up to the end point.
Journal ArticleDOI
Slicing Sets and Measures, and the Dimension of Exceptional Parameters
TL;DR: In this article, the authors improved the previously existing estimates by replacing the phrase "almost all λ" with a sharp bound for the dimension of the exceptional parameters, and showed that for almost every λ there exist positively many t∈ℝ such that λ ∈ √ t √ n √ log n ≥ 0.
Journal ArticleDOI
A simple algorithm for the fast calculation of higher order derivatives of the inverse function
TL;DR: A simple and fast recursive procedure is presented and compared with other methods known in literature both with respect to the computation time and memory usage.
Journal ArticleDOI
Divided differences of inverse functions and partitions of a convex polygon
Michael S. Floater,Tom Lyche +1 more
TL;DR: A formula for an n-th order divided difference of the inverse of a function is derived, which provides a numerically stable method of computing divided differences of k-th roots and provides a new way of enumerating all partitions of a convex polygon of a certain type.
References
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Book
An introduction to the bootstrap
Bradley Efron,Robert Tibshirani +1 more
TL;DR: This article presents bootstrap methods for estimation, using simple arguments, with Minitab macros for implementing these methods, as well as some examples of how these methods could be used for estimation purposes.
Journal ArticleDOI
Calculating Higher Derivatives of Inverses
TL;DR: The algorithm solves the weighted envy-free problem when the authors are given positive numbers a1,..., and can be also reworded into what Even and Paz call a protocol: playing 'fair', each player Pi can guarantee that pj(W4) 2 4'i(Wj) for all j E [m] even if the other players do not consistently stick to their measures.