Approximate GCD in a Bernstein basis

2019/10/04 by Corless, Robert M., Sevyeri, Leili Rafiee
#FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.1910.01998

Abstract

We adapt Victor Y. Pan's root-based algorithm for finding approximate GCD to the case where the polynomials are expressed in Bernstein bases. We use the numerically stable companion pencil of Gudbjörn F. Jónsson to compute the roots, and the Hopcroft-Karp bipartite matching method to find the degree of the approximate GCD. We offer some refinements to improve the process.

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• Approximate GCD in Lagrange bases
• Generalized companion matrix for approximate GCD
• Around the gcd of the values of two polynomials
• Simple algorithm for GCD of polynomials
• Bounds-constrained polynomial approximation using the Bernstein basis