The Lagrangian remainder of Taylor's series, distinguishes $\mathcal{O}(f(x))$ time complexities to polynomials or not

Nikolaos P. Bakas; Elias Kosmatopoulos; Mihalis Nicolaou; Savvas A. Chatzichristofis

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arXiv · 2001.11811

The Lagrangian remainder of Taylor's series, distinguishes $\mathcal{O}(f(x))$ time complexities to polynomials or not

Nikolaos P. Bakas·Elias Kosmatopoulos·Mihalis Nicolaou·Savvas A. Chatzichristofis

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Abstract

The purpose of this letter is to investigate the time complexity consequences of the truncated Taylor series, known as Taylor Polynomials \cite{bakas2019taylor,Katsoprinakis2011,Nestoridis2011}. In particular, it is demonstrated that the examination of the $\mathbf{P=NP}$ equality, is associated with the determination of whether the $n^{th}$ derivative of a particular solution is bounded or not. Accordingly, in some cases, this is not true, and hence in general.

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Nikolaos P. Bakas, Elias Kosmatopoulos, Mihalis Nicolaou, Savvas A. Chatzichristofis. 2020-01-30. The Lagrangian remainder of Taylor's series, distinguishes $\mathcal{O}(f(x))$ time complexities to polynomials or not. https://arxiv.org/abs/2001.11811

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