Numerical factorization of a polynomial by rational Hermite interpolation
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We derive a class of iterative formulae to find numerically a factor of arbitrary degree of a polynomialf(x) based on the rational Hermite interpolation. The iterative formula generates the sequence of polynomials which converge to a factor off(x). It has a high convergence order even for a factor which includes multiple zeros. Some numerical examples are also included.
Subject classificationAMS (MOS) Primary: 65D15 Secondary: 65H05
KeywordsRational Hermite interpolant root finding algorithm algebraic equation Euclidean algorithm numerical factorization
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