A One-Parameter Memoryless DFP Algorithm for Solving System of Monotone Nonlinear Equations with Application in Image Processing

Autor: Najib Ullah, Abdullah Shah, Jamilu Sabi’u, Xiangmin Jiao, Aliyu Muhammed Awwal, Nuttapol Pakkaranang, Said Karim Shah, Bancha Panyanak
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Mathematics, Vol 11, Iss 5, p 1221 (2023)
Druh dokumentu: article
ISSN: 11051221
2227-7390
DOI: 10.3390/math11051221
Popis: In matrix analysis, the scaling technique reduces the chances of an ill-conditioning of the matrix. This article proposes a one-parameter scaling memoryless Davidon–Fletcher–Powell (DFP) algorithm for solving a system of monotone nonlinear equations with convex constraints. The measure function that involves all the eigenvalues of the memoryless DFP matrix is minimized to obtain the scaling parameter’s optimal value. The resulting algorithm is matrix and derivative-free with low memory requirements and is globally convergent under some mild conditions. A numerical comparison showed that the algorithm is efficient in terms of the number of iterations, function evaluations, and CPU time. The performance of the algorithm is further illustrated by solving problems arising from image restoration.
Databáze: Directory of Open Access Journals
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