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Sparse polynomial interpolation with Bernstein polynomials

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 16 Sep 2021Publisher:The Scientific and Technological Research Council of Turkey (TUBITAK-ULAKBIM) - DIGITAL COMMONS JOURNALSJournal:TURKISH JOURNAL OF MATHEMATICS, volume 45, pages 2,103-2,107 (eissn: 1303-6149, Copyright policy )
Authors: Erdal İMAMOĞLU;

doi: 10.3906/mat-2012-65

Sparse polynomial interpolation with Bernstein polynomials

Abstract

We present an algorithm for interpolating an unknown univariate polynomial f that has a t sparse representation (t << deg(f) ) using Bernstein polynomials as term basis from 2t evaluations. Our method is based on manipulating given black box polynomial for f so that we can make use of Prony's algorithm. Scientific and Technological Research Council of Turkey (TUBTAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [119F426] The authors are supported by the Scientific and Technological Research Council of Turkey (TUBTAK) under Project 119F426.

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Keywords

Symbolic computation, sparse polynomial interpolation, Bernstein polynomials, Bernstein polynomial basis

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
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gold