DYNAMICAL SYSTEMS METHOD (DSM) AND NONLINEAR PROBLEMS

Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology

Volumn , Issue , 2005, Pages 201-228

  Ramm, A G ^a  

^a KANSAS STATE UNIVERSITY   (United States)

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EID: 33645762152     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812701589_0010     Document Type: Chapter

References (27)

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3. R. Airapetyan, A. G. Ramm, A. B. Smirnova, Continuous methods for solving nonlinear ill-posed problems, in the book “Operator theory and applications”, Amer. Math. Soc, Fields Institute Communications, Providence, RI, 2000, pp. 111-138. (editors A.G.Ramm, P.N.Shivakumar, A.V.Strauss).
4. A.B.Bakushinsky, and M.Yu. Kokurin, Iterative methods for ill-posed operator equations with smooth operators, YRSS, Moscow, 2002.(in Russian)
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7. B. Kaltenbacher, A. Neubauer, A. G. Ramm, Convergence rates of the continuous regularized Gauss-Newton method, Jour. Inv. Ill-Posed Probl., 10, N3, (2002), 261-280.
8. Kamke E., Differentialgleichungen. Losungmethoden und Losungen, Chelsea, New York, 1974.
9. J.Ortega, W.Rheinboldt, Iterative solution of nonlinear equations in several variables, SIAM, Philadelphia, 2000.
10. A. G. Ramm, Inverse problems, Springer, New York, 2005.
11. A. G. Ramm, On the discrepancy principle, Nonlinear Functional Anal, and Applic, 8, N2, (2003), 307-312.
12. A. G. Ramm, DSM for ill-posed equations with monotone operators, Comm. in Nonlinear Sci. and Numer. Simulation, 10, (2005)
13. A. G. Ramm, Dynamical systems method for solving operator equations, Communic. in Nonlinear Sci. and Numer. Simulation, 9, N2, (2004), 383-402.
14. A. G. Ramm, Inequalities for solutions to some nonlinear equations, Nonlinear Functional Anal, and Applic, 9, N2, (2004), 233-243.
15. A. G. Ramm, Discrepancy principle for the dynamical systems method, Communic. in Nonlinear Sci. and Numer. Simulation, 10, N1, (2005), 95-101
16. A. G. Ramm, Dynamical systems method for solving nonlinear operator equations International Jour, of Applied Math. Sci., 1, Nl, (2004), 97-110.
17. A. G. Ramm, Dynamical systems method and surjectivity of nonlinear maps, Communic. in Nonlinear Sci. and Numer. Simulation, 10, (2005)
18. A. G. Ramm, Dynamical systems method (DSM) for unbounded operators, Proc. Amer. Math. Soc (to appear)
19. A. G. Ramm, A nonlinear singular perturbation problem (submitted)
20. A. G. Ramm, A new discrepancy principle, Jour. Math. Anal. Appl. (to appear)
21. A. G. Ramm, Dynamical systems method and a homeomorphism theorem (submitted)
22. A. G. Ramm, Dynamical systems method for nonlinear equations in Banach spaces (submitted)
23. A. G. Ramm, A. B. Smirnova, Continuous regularized Gauss-Newton-type algorithm for nonlinear ill-posed equations with simultaneous updates of inverse derivative, Intern. Jour, of Pure and Appl Math., 2, Nl, (2002), 23-34.
24. A. G. Ramm, A. B. Smirnova, On stable numerical differentiation, Mathem. of Computation, 70, (2001), 1131-1153.
25. A. G. Ramm, A. B. Smirnova, Stable numerical differentiation: when is it possible? Jour. Korean SIAM, 7, Nl, (2003), 47-61.
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27. Tikhonov A., Leonov, A., Yagola, A., Nonlinear ill-posed problems, vol. 1, 2, Chapman and Hall, London, 1998.