An algebraic algorithm to isolate complex polynomial zeros using Sturm sequences

Computers and Mathematics with Applications

Volumn 39, Issue 3-4, 2000, Pages 95-105

  Camargo Brunetto, M A O ^a   Claudio, D M ^b   Trevisan, V ^c  

^a STATE UNIVERSITY OF LONDRINA   (Brazil)

^b PONTIFICAL CATHOLIC UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

^c FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

Author keywords

Algebraic algorithm; Polynomial zeros; Sturm sequences

Indexed keywords

ALGORITHMS; BOUNDARY VALUE PROBLEMS; COMPUTATIONAL COMPLEXITY; CONFORMAL MAPPING; DATA STRUCTURES; FUNCTIONS; OPTIMIZATION; UNIX;

ALGEBRAIC ALGORITHM; POLYNOMIAL ZEROS; STURM SEQUENCES;

POLYNOMIALS;

EID: 0034140253     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0898-1221(99)00336-3     Document Type: Article

References (12)

1. D.M. Claudio and S.M. Rump, Inclusion methods for real and complex functions in one variable, In Berichte des Forschungsschwerpunktes Informations und Kommunikationstechnik, Bericht 92.5, TUHH, Hamburg, (1992).
2. J.R. Pinkert, An exact method for finding the roots of a complex polynomial, ACM Transactions on Mathematical Software 2 (4) (December 1976).
3. H.S. Wilf, A global bisection algorithm for computing the zeros of polynomials in the complex plane, Journal of the ACM 25 (3) (1978).
4. G.E. Collins and W. Krandick, An efficient algorithm for infallible polynomial complex root isolation, In Proceedings of ISSAC '92, pp. 189-194, ACM, (1992).
5. M.A.O. Camargo-Brunetto, Algoritmos algébricos para enumerar e isolar zeros polinomiais complexes. Thesis submitted as requested to the doctor degree in Computer Science. U.F.R.G.S. (1994).
6. M. Marden, The geometry of the zeros of a polynomial in a complex variable, AMS Mathematical Surveys III (1949).
7. P. Henrici, Applied and Computational Complex Analysis, Volume 1A, Wiley and Sons, (1974).
8. D. Knuth, The Art of Computer Programming, Volume 2 - Seminumerical Algorithms, Addison-Wesley, (1981).
9. E.J. Barbeau, Polynomials, Springer-Verlag, (1989).
10. V. Trevisan, Recognition of Hurwitz polynomials., SIGSAM Bulletin 24 (4) (October 1990).
11. G.E. Collins and G.K. Loos, Real zeros of polynomials, In Computing, Suppl., Volume 4, pp. 83-94, Springer-Verlag, (1982).
12. W. Krandick, Isolierung reeler Nullstellen von Polynomen, In Wissenschaftliches Rechnen, Akademie-Verlag, Berlin, (1995).