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Analysis of zero clusters in multivariate polynomial systems
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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): 4,   Downloads (12 Months): 18,   Citation Count: 9
Additional Information:

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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

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