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 68 articles , 1 standard article )

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  1. Becker, Ruben; Sagraloff, Michael; Sharma, Vikram; Yap, Chee: A near-optimal subdivision algorithm for complex root isolation based on the Pellet test and Newton iteration (2018)
  2. Kim, Myong-Hi; Martens, Marco; Sutherland, Scott: Geometry of polynomials and root-finding via path-lifting (2018)
  3. Petković, M. S.; Petković, L. D.: Traub-Gander’s family for the simultaneous determination of multiple zeros of polynomials (2018)
  4. Vander Meulen, Kevin N.; Vanderwoerd, Trevor: Bounds on polynomial roots using intercyclic companion matrices (2018)
  5. De Terán, Fernando; Dopico, Froilán M.; Pérez, Javier: Eigenvalue condition numbers and pseudospectra of Fiedler matrices (2017)
  6. Pan, Victor Y.: Fast approximate computations with Cauchy matrices and polynomials (2017)
  7. Pan, Victor Y.; Tsigaridas, Elias: Accelerated approximation of the complex roots and factors of a univariate polynomial (2017)
  8. Pan, Victor Y.; Zhao, Liang: Real polynomial root-finding by means of matrix and polynomial iterations (2017)
  9. Gemignani, L.: Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems (2016)
  10. Nakatsukasa, Yuji; Noferini, Vanni: On the stability of computing polynomial roots via confederate linearizations (2016)
  11. Sagraloff, Michael; Mehlhorn, Kurt: Computing real roots of real polynomials (2016)
  12. Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S.: Fast and backward stable computation of roots of polynomials (2015)
  13. Kerber, Michael; Sagraloff, Michael: Root refinement for real polynomials using quadratic interval refinement (2015)
  14. Kobel, Alexander; Sagraloff, Michael: On the complexity of computing with planar algebraic curves (2015)
  15. Mehlhorn, Kurt; Sagraloff, Michael; Wang, Pengming: From approximate factorization to root isolation with application to cylindrical algebraic decomposition (2015)
  16. Pan, Victor Y.: Transformations of matrix structures work again (2015)
  17. Ruatta, Olivier; Sciabica, Mark; Szanto, Agnes: Overdetermined Weierstrass iteration and the nearest consistent system (2015)
  18. Bini, Dario A.; Robol, Leonardo: Solving secular and polynomial equations: a multiprecision algorithm (2014)
  19. De Terán, Fernando; Dopico, Froilán M.; Pérez, Javier: New bounds for roots of polynomials based on Fiedler companion matrices (2014)
  20. Pan, Victor Y.: Fast approximate computations with Cauchy matrices, polynomials and rational functions (2014)

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