ACM Portal
  Subscribe (Full Service)    Register (Limited Service, Free)    Login
  Search:   The ACM Digital Library   The Guide
  
ACM Home Page
Please provide us with feedback. Feedback
Analysis of zero clusters in multivariate polynomial systems
Full text PdfPdf (1.03 MB)
Source International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1996 international symposium on Symbolic and algebraic computation table of contents
Zurich, Switzerland
Pages: 127 - 136  
Year of Publication: 1996
ISBN:0-89791-796-0
Author
Hans J. Stetter  Tech. Univ., Vienna
Sponsors
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 6,   Downloads (12 Months): 20,   Citation Count: 9
Additional Information:

references   cited by   index terms   collaborative colleagues  

Tools and Actions: Request Permissions Request Permissions    Review this Article  
DOI Bookmark: Use this link to bookmark this Article: http://doi.acm.org/10.1145/236869.236919
What is a DOI?

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
E. Anderson , Z. Bai , C. Bischof , J. Demmel , J. Dongarra , J. Du Croz , A. Greenbaum , S. Hammarling , A. McKenney , S. Ostrouchov , D. Sorensen, LAPACK's user's guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
 
2
Thomas Becker , Volker Weispfenning , Heinz Kredel, Gro¨bner bases: a computational approach to commutative algebra, Springer-Verlag, London, 1993
 
3
HRIBERNIG, V. Sensitivity of algebraic algorithms. Ph.D. Thesis, Tech.Univ. Vienna, 1995.
 
4
V. Hribernig , H. J. Stetter, Detection and validation of clusters of polynomial zeros, Journal of Symbolic Computation, v.24 n.6, p.667-681, Dec. 1997  [doi>10.1006/jsco.1997.0160]
 
5
KAHAN, W. Conserving confluence curbs ill-condition. Tech. Rep. 6, Computer Science UC Berkeley, 1972.
6
M. G. Marinari , H. M. Möller , T. Mora, Gröbner bases of ideals given by dual bases, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.55-63, July 15-17, 1991, Bonn, West Germany  [doi>10.1145/120694.120702]
 
7
MAR1NARI, M. G., MOELLER, H. M., AND MORA., T. Groebner duality and polynomial system solving. Trans. AIDS. To appear.
 
8
H. Michael Möller , Hans J. Stetter, Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems, Numerische Mathematik, v.70 n.3, p.311-329, May 1995  [doi>10.1007/s002110050122]
 
9
STETTER, H. J. Perturbed Groebner basis representations. In preparation.
 
10
STETTER, H. J. Multivariate polynomial equations as eigenvalue problems. In Contributwns in Numerical Mathematics, vol. 2 of Series in Applicable Analysis. World Scientific, 1993, pp. 355-371.
 
11
THALLINGER, G. Analysis of zero clusters in multivariate polynomial sytems. Diploma Thesis, Tech.Univ. Vienna, 1996.

CITED BY  9
H. Michael Möller , Ralf Tenberg, Multivariate polynomial system solving using intersections of Eigenspaces, Journal of Symbolic Computation, v.32 n.5, p.513-531, November 2001
Hans J. Stetter, Stabilization of polynomial systems solving with Groebner bases, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.117-124, July 21-23, 1997, Kihei, Maui, Hawaii, United States
Robert M. Corless , Patrizia M. Gianni , Barry M. Trager, A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.133-140, July 21-23, 1997, Kihei, Maui, Hawaii, United States
Hans J. Stetter , Günther H. Thallinger, Singular systems of polynomials, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.9-16, August 13-15, 1998, Rostock, Germany
Robert M. Corless , Hiroshi Kai , Stephen M. Watt, Approximate computation of pseudovarieties, ACM SIGSAM Bulletin, v.37 n.3, September 2003
E. D. Popova , C. P. Ullrich, Simplication of symbolic-numerical interval expressions, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.207-214, August 13-15, 1998, Rostock, Germany
Barry H. Dayton , Zhonggang Zeng, Computing the multiplicity structure in solving polynomial systems, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.116-123, July 24-27, 2005, Beijing, China
Itnuit Janovitz-Freireich , Lajos Rónyai , Ágnes Szántó, Approximate radical of ideals with clusters of roots, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy
Scott R. Pope , Agnes Szanto, Nearest multivariate system with given root multiplicities, Journal of Symbolic Computation, v.44 n.6, p.606-625, June, 2009

INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms


General Terms:
Algorithms, Theory, Verification

Collaborative Colleagues:
Hans J. Stetter: colleagues

The ACM Portal is published by the Association for Computing Machinery. Copyright © 2009 ACM, Inc.
Terms of Usage   Privacy Policy   Code of Ethics   Contact Us

Useful downloads: Adobe Acrobat    QuickTime    Windows Media Player    Real Player