Computational complexity. On the geometry of polynomials and a theory of cost. I

Mike Shub; Steve Smale

Annales scientifiques de l'École Normale Supérieure (1985)

  • Volume: 18, Issue: 1, page 107-142
  • ISSN: 0012-9593

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Shub, Mike, and Smale, Steve. "Computational complexity. On the geometry of polynomials and a theory of cost. I." Annales scientifiques de l'École Normale Supérieure 18.1 (1985): 107-142. <http://eudml.org/doc/82152>.

@article{Shub1985,
author = {Shub, Mike, Smale, Steve},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Euler method; polynomial root finding; complex polynomial; number of iterations},
language = {eng},
number = {1},
pages = {107-142},
publisher = {Elsevier},
title = {Computational complexity. On the geometry of polynomials and a theory of cost. I},
url = {http://eudml.org/doc/82152},
volume = {18},
year = {1985},
}

TY - JOUR
AU - Shub, Mike
AU - Smale, Steve
TI - Computational complexity. On the geometry of polynomials and a theory of cost. I
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1985
PB - Elsevier
VL - 18
IS - 1
SP - 107
EP - 142
LA - eng
KW - Euler method; polynomial root finding; complex polynomial; number of iterations
UR - http://eudml.org/doc/82152
ER -

References

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  1. K. ATKINSON, An Introduction to Numerical Analysis, Wiley, New York, 1978. Zbl0402.65001MR80a:65001
  2. E. DURAND, Solutions Numériques de Équations Algébriques, Masson, Paris, 1960. Zbl0099.10801
  3. P. DUREN, Coefficients of Univalent Functions (Bull. Amer. Math. Soc., Vol. 83, No. 5, 1977, pp. 891-911). Zbl0372.30012MR57 #9943
  4. L. EULER, Institutiones Calculi Differentialis II, exp. IX. Opera Omnia, Serie I, Vol. X, pp. 422-455. 
  5. W. HAYMAN, Multivalent Functions, Cambridge Univ. Press : Cambridge, Eng., 1958. Zbl0082.06102
  6. P. HENRICI, Applied and Computational Complex Analysis, Wiley, New York, 1977. Zbl0363.30001MR56 #12235
  7. E. HILLE, Analytic Function Theory, II Ginn, Boston, 1962. Zbl0102.29401MR34 #1490
  8. A. S. HOUSEHOLDER, The Numerical Treatment of a Single Nonlinear equation, McGraw-Hill, New York, 1970. Zbl0242.65047MR52 #9593
  9. S. LANG, Algebra, Addison-Wesley, Reading, Mass, 1965. Zbl0193.34701MR33 #5416
  10. A. OSTROWSKI, Solutions of equations in Euclidean and Banach Spaces, Academic Press, New York, 1973. Zbl0304.65002MR50 #11760
  11. G. SAUNDERS, Thesis, U. C. Berkeley, 1982. 
  12. E. SCHRÖDER, Ueber unendlich viele Algorithmen zur Auflösing der Gleichungen (Math. Ann. 2, 1870, pp. 317-365). JFM02.0042.02
  13. S. SMALE, The Fundamental Theorem of Algebra and Complexity Theory (Bull, Amer. Math. Soc., Vol. 4, No. 1, 1981, pp. 1-36. Zbl0456.12012MR83i:65044

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