Generating approximate parametric roots of parametric polynomials

B. Curtis Eaves () and Uriel G. Rothblum
Additional contact information
B. Curtis Eaves: Stanford University
Uriel G. Rothblum: Technion—Israel Institute of Technology

Annals of Operations Research, 2016, vol. 241, issue 1, No 22, 515-573

Abstract: 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.

Keywords: Parametric polynomials; Approximate parametric roots; Newton Polygon process; Sensitivity; Puiseux fields; Algebraic plane curves; Complexity (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-014-1534-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-014-1534-5

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-014-1534-5

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().