To the generalization of the Newton-Kantorovich theorem.
Abstract
Constructive conditions for solvability are obtained, as well as an iterative scheme for finding solutions of the nonlinear equation that generalize the well-known Newton-Kantorovich theorem. The case of a nonlinear equation whose dimension does not coincide with the dimension of the unknown has been researched.
Downloads
References
Kantorovich L.V., Akilov G.P. Functional analysis. — Moscow: Nauka. — 1977. — 744 pp.
Dennis J. Schnabel R. Numerical methods of unconditional optimization and solving nonlinear equations. — Moscow: Mir. — 1988. — 440 pp.
Polyak B.T. The Newton method and its role in optimization and computational mathematics // Trudy ICA RAN. — 2006. — 28. — P. 48 — 66.
Boichuk A.A., Samoilenko A.M. Generalized inverse operators and Fredholm boundary-value problems (2-th edition). — Berlin; Boston: De Gruyter, 2016. — 298 pp.
Chuiko S.M., Boichuk I.A. An autonomous Noetherian boundary value problem in the critical case // Nonlinear Oscillations (N.Y.) — 12. — 2009. № 3, P. 405 — 416.
Chuiko S.M., Boichuk I.A., Pirus O.E. On the approximate solution of an autonomous boundary-value problem the Newton - Kantorovich method // Journal of Mathematical Sciences — 2013. — 189, № 5. — P. 867 — 881.
Chuiko S.M., Pirus O.E. On the approximate solution of autonomous boundary-value problems by the Newton method // Journal of Mathematical Sciences — 2013. — 191, № 3. — P. 449 — 464.
Gantmakher F.R. Matrix theory. — Moscow: Nauka. — 1988. — 552 pp.
Korobov V.I. Bebiya M.O. Stabilization of one class of nonlinear systems // Avtomat. i Telemekh. — 2017. — № 1. — P. 3 — 18.
Bebiya M.O. Stabilization of systems with power nonlinearity // Visnyk
of V.N.Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics. — 2014, № 1120. — Issue 69. — P. 75 — 84.
Chuiko S. Weakly nonlinear boundary value problem for a matrix differential equation // Miskolc Mathematical Notes. — 2016. — 17, № 1. — P. 139 — 150.
Campbell S.L. Singular Systems of differential equations. — San Francisco –London – Melbourne: Pitman Advanced Publishing Program. — 1980. — 178 p.
Chuiko S.M. The Green’s operator of a generalized matrix linear differentialalgebraic boundary value problem // Siberian Mathematical Journal. — 2015. —56, № 4. — P. 752 — 760.
Chuiko S.M. A generalized matrix differential-algebraic equation // Journal of Mathematical Sciences (N.Y.). – 2015. – 210, № 1. – P. 9 – 21.
Chuiko S.M. To the issue of a generalization of the matrix differentialalgebraic boundary-value problem // Journal of Mathematical Sciences. — 2017. — 227, № 1. — P. 16 — 32.
Copyright (c) 2018 S. M. Chuiko
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The copyright holder is the author.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal. (Attribution-Noncommercial-No Derivative Works licence).
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (see The Effect of Open Access).