NDLI: Chebysheff-Halley-like methods in Banach spaces

Content Provider	Springer Nature Link
Author	Argyros, Loannis K.
Copyright Year	1997
Abstract	Chebysheff-Halley methods are probably the best known cubically convergent iterative procedures for solving nonlinear equations. These methods however require an evaluation of the second Fréchet-derivative at each step which means a number of function evaluations proportional to the cube of the dimension of the space. To reduce the computational cost we replace the second Fréchet derivative with a fixed bounded bilinear operator. Using the majorant method and Newton-Kantorovich type hypotheses we provide sufficient conditions for the convergence of our method to a locally unique solution of a nonlinear equation in Banach space. Our method is shown to be faster than Newton’s method under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.
Starting Page	83
Ending Page	107
Page Count	25
File Format	PDF
ISSN	12260061
Journal	Journal of Applied Mathematics and Computing
Volume Number	4
Issue Number	1
e-ISSN	18652085
Language	English
Publisher	Springer-Verlag
Publisher Date	1997-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Chebysheff method Hally method Newton method Banach space Kantorovich hypotheses Equations with nonlinear operators Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theory of Computation Mathematics of Computing
Content Type	Text
Resource Type	Article

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