Algorithms for computation of polynomial zeros

Jan Šípek; Jan Zítko

Pokroky matematiky, fyziky a astronomie (2001)

  • Volume: 46, Issue: 1, page 33-42
  • ISSN: 0032-2423

How to cite

top

Šípek, Jan, and Zítko, Jan. "Algoritmy na výpočet kořenů polynomu." Pokroky matematiky, fyziky a astronomie 46.1 (2001): 33-42. <http://eudml.org/doc/197200>.

@article{Šípek2001,
author = {Šípek, Jan, Zítko, Jan},
journal = {Pokroky matematiky, fyziky a astronomie},
keywords = {Bairstow method; Laguerre method; Aberth method; Lehmer-Schur method; Jenkins-Traub algorithm; polynomial zeros; numerical examples; survey paper},
language = {cze},
number = {1},
pages = {33-42},
publisher = {Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists},
title = {Algoritmy na výpočet kořenů polynomu},
url = {http://eudml.org/doc/197200},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Šípek, Jan
AU - Zítko, Jan
TI - Algoritmy na výpočet kořenů polynomu
JO - Pokroky matematiky, fyziky a astronomie
PY - 2001
PB - Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists
VL - 46
IS - 1
SP - 33
EP - 42
LA - cze
KW - Bairstow method; Laguerre method; Aberth method; Lehmer-Schur method; Jenkins-Traub algorithm; polynomial zeros; numerical examples; survey paper
UR - http://eudml.org/doc/197200
ER -

References

top
  1. Bailey, D. H., A Fortran Based Multiprecision System, Tech. Report RNR-94-013, 1995. (1995) 
  2. Bell, E. T., The Development of Mathematics, McGraw–Hill, New York 1940. (1940) Zbl0025.00101MR0002768
  3. Boyer, C. A., A History of Mathematics, John Wiley & Sons, New York 1968. (1968) Zbl0182.30401MR0234791
  4. Brent, R. P., A Fortran Multiple Precision Arithmetic Package, ACM Trans. on Math. Software 4 (1978), 57–70. (1978) 
  5. Eves, H., An Introduction to the History of Mathematics, Saunders College Publishing 1983. (1983) Zbl0564.01002MR0684360
  6. Henrici, P., Elements of Numerical Analysis, John Wiley & Sons, New York 1964. (1964) Zbl0149.10901MR0166900
  7. Jenkins, M. A., Traub, J. F., A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration, Numer. Math. 14 (1970), 252–263. (1970) Zbl0176.13701MR0258271
  8. Jenkins, M. A., Traub, J. F., Algorithm 419: Zeros of a Complex Polynomial, Communications of the ACM 15 (1972), 97–110. (1972) 
  9. Knuth, D. E., The Art of Computer Programming, Volume 2 / Seminumerical Algorithms. Addison–Wesley publishing company, Inc. 1969. (1969) Zbl0191.18001MR0286318
  10. Kyurkchiev, N. V., Initial Approximations and Root Finding Methods, 1998. (1998) Zbl0904.65047MR1640837
  11. Marden, M., The Geometry of the Zeros of a Polynomial, Amer. Math. Soc., Providence, R. I. 1949. (1949) Zbl0038.15303MR0031114
  12. Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P., Numerical Recipes in FORTRAN, The Art of Scientific Computing, Second Edition. Cambridge University Press 1995. (1995) Zbl0587.65004MR1196230
  13. Parlett, B., Laguerre’s Method Applied to the Matrix Eigenvalue Problem, Math. Comp. 18 (1964), 466–485. (1964) Zbl0124.33004MR0165668
  14. Práger, M., Numerická matematika, SPN, Praha 1981. (1981) 
  15. Pan, V. Y., Solving a polynomial equation: Some history and recent progress, SIAM Rev. 39 (1997), 2, 187–220. (1997) Zbl0873.65050MR1453318
  16. Ralston, A., A first course in numerical analysis, McGraw-Hill, New York 1965. (1965) Zbl0139.31603MR0191070
  17. Vitásek, E., Numerické metody, SNTL, Praha 1987. (1987) 
  18. Wilkinson, J. H., Rounding Errors in Algebraic Processes, Notes on App. Sci. No. 32. Her Majesty’s Stationery Office 1963. (1963) Zbl1041.65502MR0161456
  19. Zítko, J., Úvod do numerické matematiky, SPN, Praha 1975. (1975) 

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.