| Asymptotic acceleration of solving multivariate polynomial systems of equations |
| Full text |
Pdf
(1.03 MB)
|
| Source
|
Annual ACM Symposium on Theory of Computing
archive
Proceedings of the thirtieth annual ACM symposium on Theory of computing
table of contents
Dallas, Texas, United States
Pages: 488 - 496
Year of Publication: 1998
ISBN:0-89791-962-9
|
|
Authors
|
|
Bernard Mourrain
|
INRIA, SAGA, BP 93, 06902 Sophia-Antipolis, France
|
|
Victor Y. Pan
|
Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY
|
|
| Sponsor |
|
| Publisher |
|
| Bibliometrics |
Downloads (6 Weeks): 4, Downloads (12 Months): 31, Citation Count: 8
|
|
|
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
|
W, Auzlnger and H,$, Stetter. An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations, In Proc. Intern. Conf. on Numerical Math., volume 86 of htt. Series of Numerical Math, pages 11-30. Blrkhauser, 1988,
|
| |
2
|
|
| |
3
|
|
| |
4
|
.I'.E Cardinal. On two iterative methods for approximating the roots of a polynomial. In J. Renegar, M. Shub, and S. Smale, editors, Proc. AMS-SIAM Summer Seminar on Math. of Numerical Analysis, (Park City, Utah, 1995), volume 32 of Lectures in Applied Math., pages 165--188. Am. Math. Soe. Press, 1996.
|
| |
5
|
J.P. Cardinal and B. Mourrain. Algebraic approach of residues and applications. In J. Reneger, M. Shub, and S. Smale, editors, Proc. AM$.SIAM Summer Seminar on Math. of Numerical Analysis, (Park City, Utah, 1995), volume 32 of Lectures in Applied Math., pages 189--210. Am. Math. Soc. Press, 1996.
|
| |
6
|
M. Elkadi and B. Mourrain. Approche Effective des R~sidus Alg6briques. Rapport de Recherche 2884, INRIA, 1996.
|
 |
7
|
|
 |
8
|
Ioanis Z. Emiris , Victor Y. Pan, The structure of sparse resultant matrices, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.189-196, July 21-23, 1997, Kihei, Maui, Hawaii, United States
[doi> 10.1145/258726.258779]
|
| |
9
|
I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky. Discriminants, Resultants and Multidimensional Determinants. Birkhiiuser, Boston-Basel-Berlin, 1994.
|
| |
10
|
|
| |
11
|
D.Kapur and Y.N. Laks~an. Elimination methods: an introducton. In B. Donald, D. Kaput, and J. Mundy, editors, $ymbolic and Numerical Computation for Artifitial Intellingence, pages 45--89. Academic Press, New York, 1992.
|
| |
12
|
ES. Macaulay. Some formulae in elimination. Prec. London Math. 5oc., 1(33):3-27, 1902.
|
| |
13
|
F.S. Macaulay. The Algebraic Theory of Modular Systems. Cambridge Univ. Press, 1916.
|
| |
14
|
B. Mourrain. Solving polynomial systems by matrix computations. Preprint, submitted, 1997.
|
| |
15
|
B. Mourrain and V. Y. Pan. Multidimensional structured matrices and polynomial systems. Calcolo, (Special Issue, Workshop on Toeplitz Matrices: Structure, Algorithms and Applications), 33:389--401, 1997.
|
| |
16
|
|
| |
17
|
B. Mourrain and V.Y. Pan. Multivariate polynomials, duality and structured matrices. Preprint, submitted for publication, 1997.
|
 |
18
|
|
| |
19
|
V.Y. Pan. Optimal and nearly optimal algorithms for appro.v,imating complex polynomial zeros. Computers and Math. Appls., 31(12):97-138, 1996.
|
| |
20
|
|
| |
21
|
P. S. Pedersen and B. $turmfels. Product formulas for resul. tents and Chow forms. Math. Zeitschrift, 214:377-396, 1993.
|
| |
22
|
|
| |
23
|
|
| |
24
|
B.L. Van der Waerden. Modern Algebra, Vol. II. Frederick Ungar Publishing Co, 1948.
|
|