Solving Polynomials with Computers

American Scientist

Volumn 86, Issue 1, 1998, Pages 62-69

  Pan, Victor Y ^a,b,c,d  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

^c STATE UNIVERSITY OF NEW YORK   (United States)

^d UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; GRAPH THEORY; INVERSE KINEMATICS; POLYNOMIALS; PROBLEM SOLVING; ROBOTIC ARMS;

LINEAR EQUATIONS; POLYNOMIAL ZEROS; QUADRATIC EQUATIONS;

COMPUTER APPLICATIONS;

EID: 0031656310     PISSN: 00030996     EISSN: None     Source Type: Trade Journal    
DOI: 10.1511/1998.17.915     Document Type: Article

References (20)

1. Atkinson, K. 1978. Introduction to Numerical Analysis. New York: Wiley.
2. Bell, E. T. 1940. The Development of Mathematics. New York: McGraw-Hill.
3. Bini, D., and V. Y. Pan. 1994. Polynomial and Matrix Computations, v.1: Fundamental Algorithms. Boston: Birkha"user.
4. Bini, D., and V. Y. Pan. 1998. Polynomial and Matrix Computations, v.2: Selected Topics Boston: Birkhäuser.
5. Bini, D., and V. Y. Pan. 1996. Graeffe's, Chebyshev-like and Cardinal's processes for splitting a polynomial into factors. Journal of Complexity 12:492-511.
6. Boyer, C. A. 1968. A History of Mathematics. New York: Wiley.
7. Cardinal, J.-P. 1996. On two iterative methods for approximating the roots of a polynomial. In Proceedings of a Workshop: Mathematics of Numerical Analysis: Real Number Algorithms, ed. J. Renegar, M. Shub and S. Smale. Lectures in Applied Mathematics 32:165-188. Providence: American Mathematical Society.
8. Cox, D., Little, J., and O'Shea, D. 1996. Ideals, Varieties and Algorithms (2nd edition). New York: Springer.
9. Gauss, G. F. 1973. Werke. New York: Band X, George Olms Verlag.
10. Henrici, P. 1974. Applied and Computational Complex Analysis, 1. New York: Wiley.
11. McNamee, J. M. 1993. A bibliography on roots of polynomials. Journal of Computational and Applied Mathematics 47(3):391-394.
12. Madsen, K. 1973. A root-finding algorithm based on Newton's method, Bit 13:71-75.
13. Neugebauer, O. 1957. The Exact Science in Antiquity (2nd edition). Providence, R.I.: Brown University Press.
14. The Numerical Algorithms Group Ltd. 1996. FRISCO - A Framework for Integrated Symbolic/ Numeric Computation. http://extweb.nag.co.uk/ projects/FRISCO.html. Main NAG site: http://www.nag.co.uk/
15. Pan, V. Y. 1987. Sequential and parallel complexity of approximate evaluation of polynomial zeros. Computers and Mathematics (with Applications) 14(8):591-622.
16. Pan, V. Y. 1994. New techniques for approximating complex polynomial zeros. Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms. New York: ACM Press; Philadelphia: SIAM Publications. pp. 260-270.
17. Pan, V. Y. 1995. Optimal (up to polylog factors) sequential and parallel algorithms for approximating complex polynomial zeros, Proceedings of the 27th Annual ACM Symposium on Theory of Computing. New York: ACM Press. pp. 741-750.
18. Pan, V. Y. 1996. Optimal and nearly optimal algorithms for approximating polynomial zeros. Computers and Mathematics (with Applications) 31:97-138.
19. Pan, V. Y. 1997. Solving a polynomial equation: Some history and recent progress. SIAM Review 39(2):187-220.
20. Smale, S. 1981. The fundamental theorem of algebra and complexity theory. Bulletin of the American Mathematical Society 4:1-36.