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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.