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Computing the common zeros of two bivariate functions via Bézout resultants

Nakatsukasa, Yuji and Noferini, Vanni and Townsend, Alex (2015) 'Computing the common zeros of two bivariate functions via Bézout resultants.' Numerische Mathematik, 129 (1). pp. 181-209. ISSN 0029-599X


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The common zeros of two bivariate functions can be computed by finding the common zeros of their polynomial interpolants expressed in a tensor Chebyshev basis. From here we develop a bivariate rootfinding algorithm based on the hidden variable resultant method and Bézout matrices with polynomial entries. Using techniques including domain subdivision, Bézoutian regularization, and local refinement we are able to reliably and accurately compute the simple common zeros of two smooth functions with polynomial interpolants of very high degree (≥ 1000). We analyze the resultant method and its conditioning by noting that the Bézout matrices are matrix polynomials. Two implementations are available: one on the Matlab Central File Exchange and another in the roots command in Chebfun2 that is adapted to suit Chebfun’s methodology.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 20 Oct 2015 13:36
Last Modified: 15 Jan 2022 00:46

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