Improved Halley-like methods for the inclusion of polynomial zeros
Copyright policy )Improved Halley-like methods for the inclusion of polynomial zeros
The authors present a method for iterative simultaneous refinement of all simple complex zeros of polynomials, when each zero is included in a disk, provided that initial approximations for all disks are available. The iterative procedure is based on calculation of Halley and Newton corrections in circular arithmetic. Such an approach is characterised by fast convergence, computational efficiency and simultaneous calculation of reliable error bounds. Numerical examples illustrate the theory.
- University of Niš Serbia
numerical examples, convergence, polynomials, Interval and finite arithmetic, centered inversion of disks, error bounds, Newton corrections, 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), circular arithmetic, Numerical computation of solutions to single equations, Halley methods, interval methods for simultaneous incluson, simple complex zeros
numerical examples, convergence, polynomials, Interval and finite arithmetic, centered inversion of disks, error bounds, Newton corrections, 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), circular arithmetic, Numerical computation of solutions to single equations, Halley methods, interval methods for simultaneous incluson, simple complex zeros
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