Design, analysis, and implementation of a multiprecision polynomial rootfinder. We present the design, analysis, and implementation of an algorithm for the computation of any number of digits of the roots of a polynomial with complex coefficients. The real and the imaginary parts of the coefficients may be integer, rational, or floating point numbers represented with an arbitrary number of digits. The algorithm has been designed to deal also with numerically hard polynomials like those arising from the symbolic preprocessing of systems of polynomial equations, where the degree and the size of the coefficients are typically huge. (netlib numeralgo na20)

References in zbMATH (referenced in 59 articles , 1 standard article )

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  1. Nakatsukasa, Yuji; Noferini, Vanni: On the stability of computing polynomial roots via confederate linearizations (2016)
  2. Sagraloff, Michael; Mehlhorn, Kurt: Computing real roots of real polynomials (2016)
  3. Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S.: Fast and backward stable computation of roots of polynomials (2015)
  4. Kerber, Michael; Sagraloff, Michael: Root refinement for real polynomials using quadratic interval refinement (2015)
  5. Kobel, Alexander; Sagraloff, Michael: On the complexity of computing with planar algebraic curves (2015)
  6. Mehlhorn, Kurt; Sagraloff, Michael; Wang, Pengming: From approximate factorization to root isolation with application to cylindrical algebraic decomposition (2015)
  7. Pan, Victor Y.: Transformations of matrix structures work again (2015)
  8. Ruatta, Olivier; Sciabica, Mark; Szanto, Agnes: Overdetermined Weierstrass iteration and the nearest consistent system (2015)
  9. Bini, Dario A.; Robol, Leonardo: Solving secular and polynomial equations: a multiprecision algorithm (2014)
  10. De Terán, Fernando; Dopico, Froilán M.; Pérez, Javier: New bounds for roots of polynomials based on Fiedler companion matrices (2014)
  11. Pan, Victor Y.: Fast approximate computations with Cauchy matrices, polynomials and rational functions (2014)
  12. Sagraloff, Michael: On the complexity of the Descartes method when using approximate arithmetic (2014)
  13. Batselier, Kim; Dreesen, Philippe; de Moor, Bart: The geometry of multivariate polynomial division and elimination (2013)
  14. Berberich, Eric; Emeliyanenko, Pavel; Kobel, Alexander; Sagraloff, Michael: Exact symbolic-numeric computation of planar algebraic curves (2013)
  15. Bini, Dario A.; Noferini, Vanni: Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method (2013)
  16. Bini, Dario A.; Noferini, Vanni; Sharify, Meisam: Locating the eigenvalues of matrix polynomials (2013)
  17. Jacobsen, Jesper Lykke; Salas, Jesús: Is the five-flow conjecture almost false? (2013)
  18. Nielsen, Johan Sejr Brinch; Simonsen, Jakob Grue: An experimental investigation of the normality of irrational algebraic numbers (2013)
  19. Pan, Victor Y.: Polynomial evaluation and interpolation and transformations of matrix structures (2013)
  20. Boyer, Robert P.; Parry, Daniel T.: On the zeros of plane partition polynomials (2012)

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