Continuous newton method and its modification

Applicable Analysis

Volumn 73, Issue 3-4, 1999, Pages 463-484

  Airapetyan, Ruban ^a  

^a KANSAS STATE UNIVERSITY   (United States)

Author keywords

47H17; 58C15; 65J15; Continuous Newton method; Exponential convergence; Frechet derivative; Integral inequality

Indexed keywords

EID: 84962022898     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036819908840791     Document Type: Article

References (14)

1. Airapetyan R.G., On new statement of inverse problem of Quantum Scattering Theory to appear
2. Airapetyan, R.G., and Puzynin, I.V., 1997. Newtonian iterative scheme with simultaneous iteractions of inverse derivations. Comp. Phys. Comm, 102: 97–108.
3. Airapetyan, R.G., Puzynin, I.V., and Zhidkov, E.P., 1997. “ Numerical method for solving the inverse problem of quantum scattering theory, in Proceedings of the Conference ”. In Inverse and Algebraic Quantum Scattering Theory Edited by: Apagyi, B., Endrédi, G., and Lévay, P., Vol. 488, 88–97. Hungary 1966
4. Airapetyan, R.G., Ramm, A.G., and Smirnova, A.B., 1999. Continuous analog of the Gauss-Newton method. Mathematical Models and Methods in Applied Sciences, 9 (N3)
5. Davidenko, D.F., 1960. On application of the parameter variation method to the inversion of the matrices. DAN SSSR, 131: 500–502.
6. Deimling, K., 1985. Nonlinear Functional Analysis, Vol. 1, Springer-Verlag.
7. Gavurin, M.K., 1958. Nonlinear functional equations and continuous analogies of interative methods. Izv. Vuzor. Ser. Matematika, 5: 18–31.
8. Kantorovich, L.V., and Akilov, G.P., 1982. “ Functional Analysis ”. Pergamon Press.
9. Ortega, J.M., and Rheinboldt, W.C., 1970. “ Iterative Solution of Nonlinear Equations in Several Variables ”. Academic Press.
10. Puzynin, I.V., Amirkhanov, I.V., Puzynina, T.P., and Zemlyanaya, E.V., 1993. The Newtonian interative scheme with simultaneous calculating the inverse operator for the derivative of nonlinear function. JINR Rapid Comms, 62: 63–73.
11. Reid, W.T., 1972. “ Riccati differential equations ”. Academic Press.
12. Szarski, J., 1967. differenital inequalities. PWN, Warszawa
13. Ulm, S., 1967. On iterative methods with the successive approximation of the inverse operator. Izv.AN Est.SSR. Ser.Fizika, Matematika, 16: 403–411.
14. Zhidkov, E.P., and Puzynin, I.V., 1967. Solving of the boundary problems for second order nonlinear differential equations by means of the stabilization method. Soviet Math. Dokl, 8: 614–616.