References
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References
-
G. Alefeld and J. Herzberger.
Introduction to Interval Computations, Computer Science and
Applied Mathematics.
Academic Press, 1983.
-
W. Auzinger and H. J. Stetter.
An Elimination Algorithm for the Computation of all Zeros of a
System of Multivariate Polynomial Equations.
In Conference in Numerical Analysis, volume 86 of ISNM,
pages 11-30. Birkhäuser, 1988.
-
Thomas Becker and Volker Weispfenning.
Gröbner Bases: A Computational Approach to Commutative
Algebra.
Springer-Verlag, 1993.
-
Bruno Buchberger and Tudor Jebelean.
Parallel Rational Arithmetic for Computer Algebra Systems:
Motivating Experiments.
Technical Report 92-29, RISC-Linz, Johannes Kepler University, Linz,
Austria, 1992.
A preliminary version was presented at the ACPC (Austrian Center for
Parallel Computation) workshop in Weinberg, Austria, April 1992.
-
B. Buchberger.
An Algorithm for Finding a Basis for the Residue Class Ring of
a Zero-Dimensional Polynomial Ideal (German).
PhD thesis, Univ. Innsbruck, Dept. of Math., Innsbruck, Austria,
1965.
-
B. Buchberger.
An algorithmic criterion for the solvability of algebraic systems of
equations (German).
Aequationes Mathematicae, 4(3):374-383, 1970.
-
B. Buchberger.
A Critical-Pair/Completion Algorithm in Reduction Rings.
In E. Börger, G. Hasenjäger, and D. Rödding, editors,
Proc. Logic and Machines: Decision Problems and Complexity, pages
137-161, 1983.
-
B. Buchberger.
A Note on the Complexity of Constructing Gröbner Bases.
In H. van Hulzen, editor, Proc. EUROCAL'83, pages 137-145,
London, England, March 1983.
-
B. Buchberger.
Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory.
In N.K. Bose, editor, Multidimensional Systems Theory, pages
184-232. D. Reidel Publishing Company, Dordrecht-Boston-Lancaster, 1985.
-
Robert M. Corless, Patrizia M. Gianni, Barry M. Trager, and Stephen M. Watt.
The Singular Value Decomposition for Polynomial Systems.
In A.H.M. Levelt, editor, ISSAC '95, pages 195-207, 1995.
-
J.C. Faugère, P. Gianni, D. Lazard, and Mora T.
Efficient Computation of Zero-Dimensional Gröbner Basis by
Change of Ordering.
JSC, 16(4):329-344, October 1993.
-
P. Gianni.
Properties of Gröbner bases under specialization.
In Proc. EUROCAL'87, Leipzig, Germany, 2-5 June 1987.
-
Hans-Gert Gräbe.
On Lucky Primes.
JSC, 15:199-209, 1993.
-
V. Hribernig and H.J. Stetter.
Detection and Validation of Clusters of Polynomial Zeros.
JSC, 11, 1995.
-
V. Hribernig.
Sensitivity of Algebraic Algorithms.
PhD thesis, TU Wien, 1994.
-
Yu-shen Huang and Wen-da Wu.
A Modified Version of an Algorithm for Solving Multivariate
Polynomial Systems.
Technical Report 5, MM Research Preprints, Academia Sinica, 1990.
-
M. Kalkbrener.
Solving systems of algebraic equations by using Gröbner bases.
In Proc. EUROCAL'87, Leipzig, Germany, 2-5 June 1987.
-
A. Kandri-Rody and D. Kapur.
Algorithms for Computing Gröbner Bases of Polynomial Ideals over
various Euclidean Rings.
In J. Fitch, editor, Proc. EUROSAM'84, pages 195-206.
Springer-Verlag, 1984.
-
A. Kandri-Rody and D. Kapur.
Computing a Gröbner Basis of Polynomial Ideals over a Euclidean
Domain.
J. Symb. Comp., 6(1):37-58, 1988.
-
D. Lazard.
Gröbner Bases, Gaussian Elimination, and Resolution of Systems of
Algebraic Equations.
In H. van Hulzen, editor, Proc. EUROCAL'83, pages 146-156,
London, England, March 1983.
-
D. Lazard.
Solving Zero-dimensional Algebraic Systems.
JSC, 13:117-131, 1992.
-
H. Michael Möller and Hans J. Stetter.
Multivariate Polynomial Equations With Multiple Zeros Solved by
Matrix Eigenproblems.
To appear in Numer. Math., ??
-
Antonio Montes.
Numerical conditioning of a system of algebraic equations with a
finite number of solutions using Gröbner bases.
SIGSAM Bulletin, 27(1):12-19, January 1993.
-
R. E. Moore.
Interval Arithmetic and Automatic Error Analysis in Digital
Computing.
PhD thesis, Mathematics Deptartement, University of Stanford, 1962.
-
G. Pauer.
On Lucky Ideals for Gröbner Basis Computations.
JSC, 14(5):471-482, November 1992.
-
A. A. Rhaman.
On the Numerical Solution of Polynomial Equations.
PhD thesis, University of Bradford, 1989.
-
Tateaki Sasaki and Matu-Tarow Noda.
Approximate Square-free Decomposition and Root-finding of
Ill-conditioned Algebraic Equations.
J. of Information Processing, 12(2), 1989.
-
Kiyoshi Shirayanagi.
An Algorithm to Compute Floating Point Gröbner Bases.
In T. Lee, editor, Mathematical Computation with Maple V: Ideas
and Applications. Birkhäuser, 1993.
-
H.J. Stetter.
Multivariate Polynomial Equations as Matrix Eigenproblems.
WSSIAA, 2:355-371, 1993.
-
H.J. Stetter.
Verification in Computer Algebra Systems.
Validation Nemerics, Computing Suppl., 9:247-263, 1993.
-
S. Stifter.
Computation of Gröbner Bases over the Integers and in General
Reduction Rings.
Master's thesis, Univ. Linz, Dept. of Math., Linz, Austria, 1985.
-
C. Traverso.
Gröbner trace algorithms.
In P. Gianni, editor, Proc. of the International Symposium on
Symbolic and Algebraic Computation, ISSAC '88, volume 358 of LNCS,
pages 125-138. Springer, 1988.
-
W. Trinks.
Über B. Buchbergers Verfahren, Systeme algebraischer Gleichungen
zu lösen (in German).
J. Number Theory, 10(4):475-488, 1978.
-
F. Winkler.
Solution of equations I: Polynomial ideals and Gröbner bases.
In Proc. Conference on Computers in Mathematics, pages
383-407, Stanford, California, USA, 1986.
-
F. Winkler.
A p-adic Approach to the Computation of Gröbner Bases.
JSC, 6(2&), 1988.
-
G. Zacharias.
Generalized Gröbner Bases in Commutative Polynomial Rings.
Master's thesis, M.I.T., Dept. of Comp. Sci., 1978.
windsteiger wolfgang
Fri Apr 12 12:20:45 MET DST 1996