The Mathematical Institute, University of Oxford, Eprints Archive

Computing the common zeros of two bivariate functions via Bezout resultants

Nakatsukasa, Yuji and Noferini, Vanni and Townsend, Alex (2013) Computing the common zeros of two bivariate functions via Bezout resultants. Technical Report. Unspecified. (Submitted)

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Abstract

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 B�ezout matrices with polynomial entries. Using techniques including domain subdivision, B�ezoutian 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 (�$\ge$ 1000). We analyze the resultant method and its conditioning by noting that the B�ezout matrices are matrix polynomials. Our robust algorithm is implemented in the roots command in Chebfun2, a software package written in object-oriented MATLAB for computing with bivariate functions.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1704
Deposited By: Lotti Ekert
Deposited On:26 Jun 2013 08:12
Last Modified:29 May 2015 19:23

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