用松弛NewtonSLRA算法近似GCD

IF 0.4 Q4 MATHEMATICS, APPLIED ACM Communications in Computer Algebra Pub Date : 2021-09-01 DOI:10.1145/3511528.3511536

Kosaku Nagasaka

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引用次数: 0

摘要

基于结构化低秩近似(SLRA)问题的求解器NewtonSLRA算法，我们提出了一种更好的单变量多项式近似最大公约数(approximate GCD)的鲁棒性和距离的算法。我们的算法主要是扩大NewtonSLRA算法中的切空间，并使其适应于一定的加权Frobenius范数。此外，我们提出了一些改进的计算时间。

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Approximate GCD by relaxed NewtonSLRA algorithm

We propose a better algorithm for approximate greatest common divisor (approximate GCD) of univariate polynomials 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 NewtonSLRA algorithm and adapts it to a certain weighted Frobenius norm. Moreover, we propose some improvement in computing time.

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