Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations
Antonevich, A. B. ; Appell, J. ; Prokhorov, V. A. ; Zabrejko, P. P.
Rendiconti del Seminario Matematico della Università di Padova, Tome 94 (1995), p. 127-141 / Harvested from Numdam
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Publié le : 1995-01-01
@article{RSMUP_1995__93__127_0,
     author = {Antonevich, A. B. and Appell, J. and Prokhorov, V. A. and Zabrejko, Pjotr},
     title = {Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {94},
     year = {1995},
     pages = {127-141},
     mrnumber = {1354354},
     zbl = {0839.65070},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1995__93__127_0}
}

Antonevich, A. B.; Appell, J.; Prokhorov, V. A.; Zabrejko, P. P. Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations. Rendiconti del Seminario Matematico della Università di Padova, Tome 94 (1995) pp. 127-141. http://gdmltest.u-ga.fr/item/RSMUP_1995__93__127_0/

[1] N. Dunford - J.T. Schwartz, Linear Operators II, Intern. Publ., Leyden (1963). | MR 188745 | MR 216303

[2] V.K. Dzjadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials (Russian), Nauka, Moscow (1977). | MR 612836 | Zbl 0481.41001

[3] M. Eiermann - X. LI - R. S. VARGA, On hybrid semi-iterative methods, SIAM J. Numer. Anal., 26 (1989), pp. 152-168. | MR 977953 | Zbl 0669.65020

[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. | MR 812617 | Zbl 0585.65025

[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. | MR 875593 | Zbl 0632.65031

[6] G.M. Goluzin, Geometrical Theory of Functions of a Complex Variable (Russian), Nauka, Moscow (1966). | MR 219714 | Zbl 0148.30603

[7] V.L. Goncharov, Theory of Interpolation and Approximation of Functions (Russian), Fizmatgiz, Moscow (1954).

[8] E. Hille, Analytic Function Theory, Vol. II, Ginn & Co., Boston (1962). | MR 201608 | Zbl 0102.29401

[9] L.V. Kantorovich - G.P. Akilov, Functional Analysis (Russian), Nauka, Moscow (1977) (Engl. transl.: Pergamon Press, Oxford (1982)). | MR 664597 | MR 511615 | Zbl 0484.46003

[10] W.V. Koppenfels - F. Stallmann, Praxis der konformen Abbildungen, Springer, Berlin (1959). | MR 107698 | Zbl 0086.28003

[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)). | MR 1038527 | Zbl 0674.47036

[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] N.S. Landkof, Elements of Modern Potential Theory (Russian), Nauka, Moscow (1966) (Engl. transl.: Springer, Berlin (1972)).

[14] M.A. Lavrentev - B.V. Shabat, Methods of the Theory of Functions of a Complex Variable (Russian), Nauka, Moscow (1973). | Zbl 0633.30001

[15] A.I. Markushevich, Theory of Analytic Functions (Russian), Nauka, Moscow (1968) (Engl. transl.: Chelsea, New York (1977)).

[16] V.I. Smirnov - N.A. Lebedev, Constructive Theory of Functions of a Complex Variable (Russian), Nauka, Moscow (1964). | MR 171926

[17] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen Co., Tokyo (1959). | MR 114894 | Zbl 0087.28401

[18] J.L. Walsh, Interpolation and Approximation By Rational Functions in the Complex Domain, Coll. Publ., Amer. Math. Soc., Providence (1960). | MR 218587 | Zbl 0106.28104

[19] P.P. Zabrejko, Error estimates for successive approximations and spectral properties of linear operators, Numer. Funct. Anal. Optim., 11 (1990), pp. 823-838. | MR 1085437 | Zbl 0733.65033

[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. | MR 1305601 | Zbl 0814.41007