Numerical factorization of a polynomial by rational Hermite interpolation
Copyright policy )Numerical factorization of a polynomial by rational Hermite interpolation
The authors derive a class of iterative formulae to find numerically a factor of arbitrary degree of a polynomial \(f(x)\) based on rational Hermite interpolation. The iterative formula generates a sequence of polynomials which converges to a factor of \(f(x)\). Local and global convergence are studied. CPU-time and the number of iterations of Bairstow's and the authors' method are compared. The best results and the low costs are obtained with the authors' algorithm. Two examples are included and commented on.
- Nagoya University Japan
numerical examples, General theory of numerical methods in complex analysis (potential theory, etc.), Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), rational Hermite interpolation, root finding algorithm, Computational aspects of field theory and polynomials, numerical factorization, local and global convergence, Numerical computation of solutions to single equations, Bairstow method
numerical examples, General theory of numerical methods in complex analysis (potential theory, etc.), Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), rational Hermite interpolation, root finding algorithm, Computational aspects of field theory and polynomials, numerical factorization, local and global convergence, Numerical computation of solutions to single equations, Bairstow method
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