A mesh independence principle for perturbed Newton-like methods and their discretizations

Journal of Applied Mathematics and Computing

Volumn 7, Issue 1, 2000, Pages 139-159

  Argyros, Ioannis K ^a  

^a CAMERON UNIVERSITY   (United States)

Author keywords

Banach space; Discretized iterations; Inexact Newton like methods; Mesh independence; Operator equations

Indexed keywords

BANACH SPACES; BOUNDARY VALUE PROBLEMS; MATHEMATICAL OPERATORS; MESH GENERATION; NEWTON-RAPHSON METHOD;

DISCRETIZED ITERATIONS; INEXACT NEWTONS; MESH INDEPENDENCE; NEWTON LIKE METHODS; NEWTON'S METHODS; NONLINEAR OPERATOR EQUATIONS; OPERATOR EQUATION; UNIFORM DISCRETIZATION;

NONLINEAR EQUATIONS;

EID: 84892915838     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf03009933     Document Type: Article

References (11)

1. E.L. Allgower, K. Böhmer, F.A. Potra, and W.C. Rheinboldt, A mesh-independence principle for operator equations and their discretizations, SIAM J. Numer. Anal. 23 1, (1986), 160-169.
2. I.K. Argyros, A mesh independence principle for operator equations and their discretizations under mild differentiability conditions, Computing 45 (1990), 265-268.
3. I.K. Argyros, On the discretization of Newton-like methods, Internat. J. Computer. Math. 52 (1994), 161-170.
4. I.K. Argyros, A unified approach for constructing fast two-step Newton-like methods, Monatshefte für Mathematik 119 (1995), 1-22.
5. I.K. Argyros, A unified approach for constructing fast two-step methods in Banach space and their applications, Comp. Appl. Math. Proc. CAM96 (1996), 1-50.
6. L. Collatz, The Numerical Treatment of Differential Equations, Grundlehren der Mathematik, Bd 8, 2nd edition. Springer-Verlag, Heidelberg, 1959.
7. L.V. Kantorovich and E.P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, New York, 1964.
8. F.A. Potra and V. Ptak, Sharp error bounds for Newton's process, Numer. Math. 34 (1980), 63-72.
9. F.A. Potra, On an iterative algorithm of order 1.839. . . for solving nonlinear operator equations, Numer. Funct. Anal. and Optimiz. 7(1) (1984-85), 75-106.
10. G.M. Vainikko, Galerkin's perturbation method and the general theory of approximate methods for non-linear equations, USSR Comp. Math. and Math. Phys. 4 (1967), 723-751.
11. P.P. Zabrejko and D.F. Nguen, The majorant method in the theory of Newton-Kantorovich approximations and the Ptak error estimates, Numer. Funct. Anal. And Optimiz. 9 (5 and 6), (1987), 671-684.