|
Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 10, Pages 1757–1764
(Mi zvmmf4766)
|
|
|
|
This article is cited in 4 scientific papers (total in 4 papers)
Gradient projection method for stable approximation of quasisolutions to irregular nonlinear operator equations
A. I. Kozlov, M. Yu. Kokurin Mari State University, pl. Lenina 1, Yoshkar-Ola, 424001, Russia
Abstract:
An iterative process of the gradient projection type is constructed and examined as a tool for approximating quasisolutions to irregular nonlinear operator equations in a Hilbert space. One step of this process combines a gradient descent step in a finite-dimensional affine subspace and the Fejrér operator with respect to the convex closed set to which the quasisolution belongs. It is proved that the approximations generated by the proposed method stabilize in a small neighborhood of the desired quasisolution, and the diameter of this neighborhood is estimated.
Key words:
irregular nonlinear operator equations, quasisolution, iterative methods, convergence, stability.
Received: 22.12.2008
Citation:
A. I. Kozlov, M. Yu. Kokurin, “Gradient projection method for stable approximation of quasisolutions to irregular nonlinear operator equations”, Zh. Vychisl. Mat. Mat. Fiz., 49:10 (2009), 1757–1764; Comput. Math. Math. Phys., 49:10 (2009), 1678–1685
Linking options:
https://www.mathnet.ru/eng/zvmmf4766 https://www.mathnet.ru/eng/zvmmf/v49/i10/p1757
|
Statistics & downloads: |
Abstract page: | 443 | Full-text PDF : | 104 | References: | 47 | First page: | 7 |
|