Approximate GCD in Lagrange bases

Sevyeri, Leili Rafiee; Corless, Robert M.

doi:10.1109/synasc51798.2020.00018

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2025

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Cited by 3 publications

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“…the subresultant matrix). Moreover, we note that there are also algorithms [31,32,4,21,28,7] using other bases (e.g. the Bernstein basis) instead of the monomial basis.…”

Section: Introductionmentioning

confidence: 99%

Relaxed NewtonSLRA for Approximate GCD

Nagasaka

2021

Computer Algebra in Scientific Computing

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We propose a better algorithm for approximate GCD in terms of robustness and distance, based on the NewtonSLRA algorithm that is a solver for the structured low rank approximation (SLRA) problem. Our algorithm mainly enlarges the tangent space in the Newton-SLRA algorithm and adapts it to a certain weighted Frobenius norm. By this improvement, we prevent a convergence to a local optimum that is possibly far from the global optimum. We also propose some modification using a sparsity on the NewtonSLRA algorithm for the subresultant matrix in terms of computing time.

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“…the subresultant matrix). Moreover, we note that there are also algorithms [31,32,4,21,28,7] using other bases (e.g. the Bernstein basis) instead of the monomial basis.…”

Section: Introductionmentioning

confidence: 99%