Un calcul numérique des solutions isolées d'un système polynomial de plusieurs variables complexes

Bui Doan Khanh

RAIRO - Operations Research - Recherche Opérationnelle (1991)

  • Volume: 25, Issue: 3, page 277-289
  • ISSN: 0399-0559

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Khanh, Bui Doan. "Un calcul numérique des solutions isolées d'un système polynomial de plusieurs variables complexes." RAIRO - Operations Research - Recherche Opérationnelle 25.3 (1991): 277-289. <http://eudml.org/doc/105015>.

@article{Khanh1991,
author = {Khanh, Bui Doan},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {isolated solutions; polynomial system of several complex variables; systems of polynomial equations; homotopy continuation method; zeros of an analytic function; root finding; numerical multiple solutions; Rouché’s theorem; Hermite predictor-corrector scheme},
language = {fre},
number = {3},
pages = {277-289},
publisher = {EDP-Sciences},
title = {Un calcul numérique des solutions isolées d'un système polynomial de plusieurs variables complexes},
url = {http://eudml.org/doc/105015},
volume = {25},
year = {1991},
}

TY - JOUR
AU - Khanh, Bui Doan
TI - Un calcul numérique des solutions isolées d'un système polynomial de plusieurs variables complexes
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1991
PB - EDP-Sciences
VL - 25
IS - 3
SP - 277
EP - 289
LA - fre
KW - isolated solutions; polynomial system of several complex variables; systems of polynomial equations; homotopy continuation method; zeros of an analytic function; root finding; numerical multiple solutions; Rouché’s theorem; Hermite predictor-corrector scheme
UR - http://eudml.org/doc/105015
ER -

References

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  1. 1. Bui DOAN KHANH, Un calcul numérique des différentes solutions d'un système d'équations non linéaires, RAIRO Rech. Opèr., 1990, 24, p. 159-166. Zbl0707.65032MR1065532
  2. 2. S. N. CHOW, J. MALLET-PARET et J. A. JORKE, Finding Zeros of Maps: Homotopy Methods that are Constructive with Probability One , Math. Comp., 1978, 32, p. 887-899. Zbl0398.65029MR492046
  3. 3. S.N. CHOW, J. MALLET-PARET et J. A. JORKE, A Homotopy Method for Locating All Zeros of a System of Polynomials, in Functional Differential Equations and Approximation ofixed Points, Lecture Notes in Math., H. O. PEITGEN et H. O. WALTHER éd., 1979, n°730, p. 228-237. Zbl0427.65034
  4. 4. A. P. HULMAN et H. E. SALZER, Roots of sin(z) = z, Philos. Mag., 1943, 34, p. 575. Zbl0061.30103
  5. 5. T. Y. Li, T. SHAUR et J. A. JORKE, Numerically Determining Solution of Systems of Polynomial Equations, Bull. Amer. Math. Soc., 1988 18, p. 173-177. Zbl0651.65042MR929095
  6. 6. A. P. MORGAN, A Method for Computing All Solutions to Systems of Polynomial Equations, ACM Trans. Math. Software, 1983 9, p. 1-17. Zbl0516.65026MR715803
  7. 7. A. P. MORGAN, A Transformation to Avoid Solutions at Infinity for Polynomial Systems, Appl. Math. Comput., 1986 18, p. 77-86. Zbl0597.65045MR815773
  8. 8. A. P. MORGAN, Solving Polynomial Systems Using Continuation for Scientific and Engineering Problems, Prentice-Hall, N. J., 1987. Zbl0733.65031
  9. 9. A. P. MORGAN et A. SOMMESE, Computing all Solutions to Polynomial Systems using Homotopy Continuation, Appl. Math. Comput., 1987, 24, p. 115-138. Zbl0635.65058MR914807
  10. 10. L. PIEGL, Geometric Method of Intersecting Natural Quadratics Represented in Trimmed SurfaceForm, Comput. Aided Design, 1989, 21, p. 201-212. Zbl0673.65007
  11. 11. T. W. SEDERBERG, Algorithm for Algebraic Curve Intersection, Comput. Aided Design, 1989, 21, p. 547-554. Zbl0688.65012
  12. 12. L. T. WATSON, S. C. BILLUPS et A. P. MORGAN, Hompack: a Suite of Codes for Globally Convergent Homotopy Algorithm, ACM Trans. Math. Software, 1987, 13, p. 281-310. Zbl0626.65049MR918581
  13. 13. A. H. WRIGHT, Finding all Solutions to a System of Polynomial Equations, Math.Comp., 1985, 44, p. 125-133. Zbl0567.55002MR771035
  14. 14. W. ZULEHNER, A Simple Homotopy Method for Determining all Isolated Solutions to Polynomial Systems, Math. Comp., 1988, 50, p. 167-177. Zbl0637.65045MR917824

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