Iterative approximation of fixed points and applications to two-point second-order boundary value problems and to machine learning
Küçük Resim Yok
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper, we revisit two recently published papers on the iterative approximation of fixed points by Kumam et al. (2019) [17] and Maniu (2020) [19] and reproduce convergence, stability, and data dependency results presented in these papers by removing some strong restrictions imposed on parametric control sequences. We confirm the validity and applicability of our results through various non-trivial numerical examples. We suggest a new method based on the iteration algorithm given by Thakur et al. (2014) [28] to solve the two-point second-order boundary value problems. Furthermore, based on the above mentioned iteration algorithm and S-iteration algorithm, we propose two new gradient type projection algorithms and applied them to supervised learning. In both applications, we present some numerical examples to demonstrate the superiority of the newly introduced methods in terms of convergence, accuracy, and computational time against some earlier methods. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
Açıklama
Anahtar Kelimeler
Convergence, Stability, Data Dependence, Boundary Value Problem, Supervised Learning, Machine Learning, Convergence
Kaynak
Applied Numerical Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
167
