Detection and validation of clusters of polynomial zeros

Journal of Symbolic Computation

Volumn 24, Issue 6, 1997, Pages 667-681

  Hribernig, V ^a   Stetter, H J ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031539450     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1997.0160     Document Type: Article

References (16)

1. Davenport, J.H., Siret, Y., Tournier, E. (1993). Computer Algebra. Systems and Algorithms for Algebraic computation. New York: Academic Press.
2. Hribernig, V. (1994). Sensitivity of Algebraic Algorithms. Ph.D. Thesis at the Technical University of Vienna.
3. Hull, T.E., Mathon, R. (1996). The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence. ACM Trans. Numer. Software 22, 261-280.
4. Kahan, W. (1972): Conserving confluence curbs ill-condition. CS Technical Report 6, University of California, Berkeley.
5. Koh-Trefethen, L.N. (1994). Pseudozeros of polynomials and pseudospectra of companion matrices. Numer. Math. 68, 403-425.
6. Möller, H.M., Stetter, H.J. (1994). Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems. Numer. Math. 70, 311-329.
7. Mosier, R.G. (1986). Root neighbourhoods of a polynomial. Math. Comput. 47, 265-273.
8. Neumaier, A. (1988). An existence test for root clusters and multiple roots. ZAMM 68, 256-257.
9. Neumaier, A. (1990). Interval Methods for Systems of Equations. Cambridge: Cambridge University Press.
10. Rhaman, A.A. (1989). On the Numerical Solution of Polynomial Equations. Ph.D. Thesis at the University of Bradford, U.K.
11. Sasaki, T., Noda, M.T. (1989). Approximate square-free decomposition and rootfinding for ill-conditioned algebraic equations. J. Inf. Proc. 12, 139-168.
12. Schoenhage, A. (1985). Quasi-GCD computations. Journal of Complexity 1, 118-137.
13. Schwarz, H.R. (1988). Numerische Mathematik. Stuttgart: B.G. Teubner
14. Stetter, H.J. (1993a). Verification in computer algebra systems. Validation Numerics. Computing Suppl. 9, 247-263.
15. Stetter, H.J. (1993b). Multivariate polynomial equations as matrix eigenproblems. Contributions in Numerical Mathematics. World Scientific: Series in Applicable Analysis 2, 355-371.
16. Stetter, H. J. (1996). Analysis of zero clusters in multivariate systems. Proceedings of ISSAC '96. ACM Press, New York.