On general iterative methods for the solutions of a class of nonlinear operator equations
Author:
M. Z. Nashed
Journal:
Math. Comp. 19 (1965), 1424
MSC:
Primary 65.10
MathSciNet review:
0179906
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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 M. Altman, "A general method of steepest orthodescent," Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., v. 9, 1961, p. 645651. MR 25 #7526. MR 0137298 (25:752b)
 [2]
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 [3]
 L. M. Graves, "Riemann integration and Taylor's theorem in general analysis," Trans. Amer. Math. Soc., v. 29, 1927, p. 163177.
 [4]
 R. M. Hayes, "Iterative methods of solving linear problems on Hilbert space," Contributions to the Solution of Systems of Linear Equations and the Determination of Eigenvalues, Nat. Bur. Standards Appl. Math. Ser., No. 39, U. S. Government Printing Office, Washington, D. C, 1954, p. 71103. MR 16, 597. MR 0066563 (16:597b)
 [5]
 M. R. Hestenes, "Hilbert space methods in variation theory and numerical analysis," Proc. Internat. Congress of Mathematicians, v. 3, 1954, p. 229236.
 [6]
 A. S. Householder & F. L. Bauer, "On certain iterative methods for solving linear systems," Numer. Math., v. 2, 1960, p. 5559. MR 22 #7251. MR 0116464 (22:7251)
 [7]
 L. V. Kantorovich & G. P. Akilov, Functional Analysis in Normed Spaces, Fizmatgiz, Moscow, 1959. (Russian) MR 22 #9837. MR 0119071 (22:9837)
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 [12]
 M. Z. Nashed, "Iterative methods for the solutions of nonlinear operator equations in Hilbert space," Ph. D. Dissertation, The University of Michigan, Ann Arbor, Mich., 1963.
 [13]
 M. Z. Nashed, "The convergence of the method of steepest descents for nonlinear equations with variational or quasivariational operators," J. Math. Mech., v. 13, 1964, p. 765794. MR 0166638 (29:3911)
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 W. V. Petryshyn, "Direct and iterative methods for the solution of linear operator equations in Hilbert space," Trans. Amer. Math. Soc., v. 105, 1962, p. 136175. MR 26 #3180. MR 0145651 (26:3180)
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 M. M. Vaĭnberg, Variational Methods for Investigation of NonLinear Operators, GITTL, Moscow, 1956. (Russian) MR 19, 567.
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 M. M. Vaĭnberg, "On the convergence of the method of steepest descents for nonlinear equations," Dokl. Akad. Nauk SSSR, v. 130, 1960, p. 912. Soviet Math Dokl., v. 1, 1960, p. 14. MR 25 #751.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196501799064
PII:
S 00255718(1965)01799064
Article copyright:
© Copyright 1965
American Mathematical Society
