Download PDFOpen PDF in browserComputing Multiple Roots of Polynomials in Stochastic Arithmetic with Newton Method and Approximate GCDEasyChair Preprint 71847 pages•Date: December 7, 2021AbstractIn this article, we propose new methods to compute multiple roots of polynomials in floating-point arithmetic. We rely on stochastic arithmetic that makes it possible to deal with rounding errors. We develop the concept of stochastic GCD that we use to deflate a polynomial in order to obtain a polynomial with single roots. We can then apply Newton method to get fast and accurate approximations of the roots. Numerical experiments show the effectiveness and efficiency of our methods. Keyphrases: Approximate GCD, Discrete Stochastic Arithmetic, Newton method, floating-point arithmetic, numerical validation, rounding errors
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