Polynomial approximation on disjoint segments and amplification of approximation

Yuri Malykhin; Konstantin Ryutin

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arXiv · 2306.11613

Polynomial approximation on disjoint segments and amplification of approximation

Yuri Malykhin·Konstantin Ryutin

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Abstract

We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical analysis, complexity theory, quantum algorithms, etc. The one, most relevant for us, is the amplification of approximation method: it allows to construct approximations of higher degree $M$ and better accuracy from the approximations of degree $m$.

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BibTeX RIS

Yuri Malykhin, Konstantin Ryutin. 2023-06-20. Polynomial approximation on disjoint segments and amplification of approximation. https://arxiv.org/abs/2306.11613

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