A Descartes algorithm for polynomials with bit-stream coefficients

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3718 LNCS, Issue , 2005, Pages 138-149

  Eigenwillig, Arno ^a   Kettner, Lutz ^a   Krandick, Werner ^b   Mehlhorn, Kurt ^a   Schmitt, Susanne ^a   Wolpert, Nicola ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^b Drexel University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; LINEAR ALGEBRA; MATHEMATICAL OPERATORS; PROBLEM SOLVING;

BINARY POINT; COEFFICIENT APPROXIMATIONS; DESCARTES ALGORITHM;

POLYNOMIAL APPROXIMATION;

EID: 33744932718     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11555964_12     Document Type: Conference Paper

References (19)

1. Collins, G.E., Akritas, A.G.: Polynomial real root isolation using Descartes' rule of signs. In Jenks, R.D., ed.: Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation, ACM Press (1976) 272-275
2. Uspensky, J.: Theory of Equations. McGraw-Hill (1948)
3. Krandick, W.: Isolierung reeller Nullstellen von Polynomen. In Herzberger, J., ed.: Wissenschaftliches Rechnen. Akademie-Verlag (1995) 105-154
4. Rouillier, F., Zimmermann, P.: Efficient isolation of a polynomial's real roots. J. Computational and Applied Mathematics 162 (2004) 33-50
5. Lane, J.M., Riesenfeld, R.F.: Bounds on a polynomial. BIT 21 (1981) 112-117
6. Mourrain, B., Vrahatis, M.N., Yakoubsohn, J.C.: On the complexity of isolating real roots and computing with certainty the topological degree. J. Complexity 18 (2002) 612-640
7. Basu, S., Pollack, R., Roy, M.F.: Algorithms in Real Algebraic Geometry. Springer (2003)
8. Mourrain, B., Rouillier, F., Roy, M.F.: Bernstein's basis and real root isolation. Rapport de recherche 5149, INRIA-Rocquencourt (2004) http://www.inria.fr/rrrt/rr-5149.html.
9. Collins, G.E., Johnson, J.R., Krandick, W.: Interval arithmetic in cylindrical algebraic decomposition. J. Symbolic Computation 34 (2002) 143-155
10. Henrici, P.: Applied and Computational Complex Analysis. Volume 1. Wiley (1974)
11. Weyl, H.: Randbemerkungen zu Hauptproblemen der Mathematik II: Fundamentalsatz der Algebra und Grundlagen der Mathematik. Math. Z. 20 (1924) 131-152
12. Pan, V.: Solving a polynomial equation: Some history and recent progress. SIAM Review 39 (1997) 187-220
13. Pan, V.: Univariate polynomials: Nearly optimal algorithms for numerical factorization and root finding. J. Symbolic Computation 33 (2002) 701-733
14. Prautzsch, H., Boehm, W., Paluszny, M.: Bézier and B-Spline Techniques. Springer (2002)
15. Hoschek, J., Lasser, D.: Fundamentals of computer aided geometric design. A K Peters (1996) Translation of: Grundlagen der geometrischen Datenverarbeitung, Teubner, 1989.
16. Krandick, W., Mehlhorn, K.: New bounds for the Descartes method. Technical report, Drexel University, Dept. of Computer Science (2004) to appear in J. Symbolic Computation, http://www.es.drexel.edu/static/reports/DU-CS-04-04.html.
17. Smith, B.T.: Error bounds for zeros of a polynomial based upon Gerschgorin's theorems. J. ACM 17 (1970) 661-674
18. Bini, D.A., Florentino:, G.: Design, analysis, and implementation of a multiprecision polynomial rootfinder. Numerical Algorithms 23 (2000) 127-173
19. Yap, C.K.: Fundamental Problems of Algorithmic Algebra. Oxford University Press (2000)