Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations

A. B. Antonevich; J. Appell; V. A. Prokhorov; P. P. Zabrejko

Rendiconti del Seminario Matematico della Università di Padova (1995)

  • Volume: 93, page 127-141
  • ISSN: 0041-8994

How to cite

top

Antonevich, A. B., et al. "Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations." Rendiconti del Seminario Matematico della Università di Padova 93 (1995): 127-141. <http://eudml.org/doc/108351>.

@article{Antonevich1995,
author = {Antonevich, A. B., Appell, J., Prokhorov, V. A., Zabrejko, P. P.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {operator equation; Banach space; Chebyshev quasi-iteration method; convergence; error estimates},
language = {eng},
pages = {127-141},
publisher = {Seminario Matematico of the University of Padua},
title = {Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations},
url = {http://eudml.org/doc/108351},
volume = {93},
year = {1995},
}

TY - JOUR
AU - Antonevich, A. B.
AU - Appell, J.
AU - Prokhorov, V. A.
AU - Zabrejko, P. P.
TI - Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1995
PB - Seminario Matematico of the University of Padua
VL - 93
SP - 127
EP - 141
LA - eng
KW - operator equation; Banach space; Chebyshev quasi-iteration method; convergence; error estimates
UR - http://eudml.org/doc/108351
ER -

References

top
  1. [1] N. Dunford - J.T. Schwartz, Linear Operators II, Intern. Publ., Leyden (1963). MR216303
  2. [2] V.K. Dzjadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials (Russian), Nauka, Moscow (1977). Zbl0481.41001MR612836
  3. [3] M. Eiermann - X. LI - R. S. VARGA, On hybrid semi-iterative methods, SIAM J. Numer. Anal., 26 (1989), pp. 152-168. Zbl0669.65020MR977953
  4. [4] M. Eiermann - W. NIETHAMMER - R. S. VARGA, A study of semi-iterative methods for nonsymmetric systems of linear equations, Numer. Math., 47 (1985), pp. 505-533. Zbl0585.65025MR812617
  5. [5] M. Eiermann - R.S. Varga - W. Niethammer, Iterationsverfahren für nichtsymmetrische Gleichungssysteme und Approximationsmethoden im Komplexen, Jber. Dt. Math. Vgg., 89 (1987), pp. 1-32. Zbl0632.65031MR875593
  6. [6] G.M. Goluzin, Geometrical Theory of Functions of a Complex Variable (Russian), Nauka, Moscow (1966). Zbl0148.30603MR219714
  7. [7] V.L. Goncharov, Theory of Interpolation and Approximation of Functions (Russian), Fizmatgiz, Moscow (1954). 
  8. [8] E. Hille, Analytic Function Theory, Vol. II, Ginn & Co., Boston (1962). Zbl0102.29401MR201608
  9. [9] L.V. Kantorovich - G.P. Akilov, Functional Analysis (Russian), Nauka, Moscow (1977) (Engl. transl.: Pergamon Press, Oxford (1982)). Zbl0484.46003MR511615
  10. [10] W.V. Koppenfels - F. Stallmann, Praxis der konformen Abbildungen, Springer, Berlin (1959). Zbl0086.28003MR107698
  11. [11] M.A. Krasnosel'skij - Je A. Lifshits - A.V. Sobolev: Positive Linear Systems - The Method of Positive Operators (Russian), Nauka, Moscow (1985) (Engl. transl.: Heldermann, Berlin (1989)). Zbl0674.47036MR1038527
  12. [12] M.A. Krasnosel'skij - G.M. Vajnikko - P.P. Zabrejko - Ja B. Rutit-Skij - V. Ja.STETSENKO, Approximate Solutions of Operator Equations (Russian), Nauka, Moscow (1969) (Engl. transl.: Noordhoff, Groningen (1972)). 
  13. [13] N.S. Landkof, Elements of Modern Potential Theory (Russian), Nauka, Moscow (1966) (Engl. transl.: Springer, Berlin (1972)). 
  14. [14] M.A. Lavrentev - B.V. Shabat, Methods of the Theory of Functions of a Complex Variable (Russian), Nauka, Moscow (1973). Zbl0633.30001
  15. [15] A.I. Markushevich, Theory of Analytic Functions (Russian), Nauka, Moscow (1968) (Engl. transl.: Chelsea, New York (1977)). 
  16. [16] V.I. Smirnov - N.A. Lebedev, Constructive Theory of Functions of a Complex Variable (Russian), Nauka, Moscow (1964). Zbl0164.37503MR171926
  17. [17] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen Co., Tokyo (1959). Zbl0087.28401MR114894
  18. [18] J.L. Walsh, Interpolation and Approximation byRational Functions in the Complex Domain, Coll. Publ., Amer. Math. Soc., Providence (1960). Zbl0106.28104MR218587
  19. [19] P.P. Zabrejko, Error estimates for successive approximations and spectral properties of linear operators, Numer. Funct. Anal. Optim., 11 (1990), pp. 823-838. Zbl0733.65033MR1085437
  20. [20] A.P. Zabrejko - P.P. Zabrejko, Chebyshev polynomial iterations and approximate solutions of linear operator equations, Zeitschr. Anal. Anw., 13 (1994), pp. 667-681. Zbl0814.41007MR1305601

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.