Dynamical systems method for solving operator equations

Communications in Nonlinear Science and Numerical Simulation

Volumn 9, Issue 4, 2004, Pages 383-402

  Ramm, A G ^a  

^a KANSAS STATE UNIVERSITY   (United States)

Author keywords

Dynamical systems method; Global solution; Ill posed problem; Operator equation

Indexed keywords

MATHEMATICAL OPERATORS; NONLINEAR SYSTEMS; PROBLEM SOLVING; THEOREM PROVING;

CAUCHY PROBLEMS; OPERATOR EQUATIONS;

LINEAR SYSTEMS;

DYNAMICAL SYSTEM;

EID: 1642570232     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1007-5704(03)00006-6     Document Type: Article

References (18)

1. Airapetyan R. Ramm A.G. Smirnova A.B. Continuous analog of Gauss-Newton method Math. Models Meth. Appl. Sci. 9 3 1999 463-474
2. Airapetyan R. Ramm A.G. Dynamical systems and discrete methods for solving nonlinear ill-posed problems Anastassiou G. (Ed.) Applied mathematical reviews vol. 1 2000 491-536 World Scientific Publishers
3. Airapetyan R. Ramm A.G. Smirnova A.B. Continuous methods for solving nonlinear ill-posed problems Ramm A.G. Shivakumar P.N. Strauss A.V. Operator theory and applications 2000 111-138 American Mathematical Society, Fields Institute Communications Providence, RI
4. Kaltenbacher B. Neubauer A. Ramm A.G. Convergence rates of the continuous regularized Gauss-Newton method J. Inv. Ill-Posed Prob. 10 3 2002 261-280
5. Ramm A.G. Smirnova A.B. A numerical method for solving nonlinear ill-posed problems Nonlinear Func. Anal. Opt. 20 3 1999 317-332
6. Ramm A.G. Smirnova A.B. On stable numerical differentiation Math. Comput. 70 2001 1131-1153
7. Ramm A.G. Linear ill-posed problems and dynamical systems J. Math. Anal. Appl. 258 1 2001 448-456
8. Ramm A.G. Smirnova A.B. Continuous regularized Gauss-Newton-type algorithm for nonlinear ill-posed equations with simultaneous updates of inverse derivative Int. J. Pure Appl. Math. 2 1 2002 23-34
9. Ramm A.G. A numerical method for some nonlinear problems Math. Models Meth. Appl. Sci. 9 2 1999 325-335
10. Ramm A.G. Acceleration of convergence of a continuous analog of the Newton method Appl. Anal. 81 4 2002 1001-1004
11. Ramm A.G. Regularization of ill-posed problems with unbounded operators J. Math. Anal. Appl. 271 2001 547-550
12. Ramm A.G. On equations of the first kind Diff. Equat. 4 1968 2056-2060
13. Ramm A.G. Stable solutions of some ill-posed problems Math. Meth. Appl. Sci. 3 1981 336-363
14. Alber Ya. Continuous Newton-type processes Diff. Uravn. 7 1 1971 1931-1945
15. Deimling K. Nonlinear functional analysis 1985 Springer Berlin
16. Alber Ya. Ryasantseva I. On regularized evolution equations Func. Diff. Equat. 7 2000 177-187
17. Ramm A.G. Galstian A. On deconvolution methods Internal. J. of Engin. Sci. 41 N1 2003 31-43
18. Ramm A.G. Smirnova A.B. Favini A. Continuous modified Newton's-type method for nonlinear operator equations Ann di Mat Pure Appl 182 N1 2003 37-52