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Generating approximate parametric roots of parametric polynomials

Author

Listed:
  • B. Curtis Eaves

    (Stanford University)

  • Uriel G. Rothblum

    (Technion—Israel Institute of Technology)

Abstract

Built upon a ground field is the parametric field, the Puiseux field, of semi-terminating formal fractional power series. A parametric polynomial is a polynomial with coefficients in the parametric field, and roots of parametric polynomials are parametric. For a parametric polynomial with nonterminating parametric coefficients and a target accuracy, using sensitivity of the Newton Polygon process, a complete set of approximate parametric roots, each meeting target accuracy, is generated. All arguments are algebraic, from the inside out, self-contained, penetrating, and uniform in that only the Newton Polygon process is used, for both preprocessing and intraprocessing. A complexity analysis over ground field operations is developed; setting aside root generation for ground field polynomials, but bounding such, polynomial bounds are established in the degree of the parametric polynomial and the target accuracy.

Suggested Citation

  • B. Curtis Eaves & Uriel G. Rothblum, 2016. "Generating approximate parametric roots of parametric polynomials," Annals of Operations Research, Springer, vol. 241(1), pages 515-573, June.
    • Handle: RePEc:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-014-1534-5
    DOI: 10.1007/s10479-014-1534-5
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    References listed on IDEAS

    as
    1. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
    2. B. Curtis Eaves & Uriel G. Rothblum, 1989. "A Theory on Extending Algorithms for Parametric Problems," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 502-533, August.
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