Advances in the Semilocal Convergence of Newton’s Method with Real-World Applications

Mathematics

Lara Orcos¹  Á.Alberto Magreñán²  IoannisK. Argyros³  Íñigo Sarría⁴ 

[1] Departamento de Matemática Aplicada, Universidad Politècnica de València, 46022 València, Spain;Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain;Department of Mathematics Sciences Lawton, Cameron University, Lawton, OK 73505, USA;Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño;

关键词: Banach space;    Newton’s method;    semi-local convergence;    Kantorovich hypothesis;   

DOI  :  10.3390/math7030299

来源: DOAJ

【 摘 要 】

The aim of this paper is to present a new semi-local convergence analysis for Newton’s method in a Banach space setting. The novelty of this paper is that by using more precise Lipschitz constants than in earlier studies and our new idea of restricted convergence domains, we extend the applicability of Newton’s method as follows: The convergence domain is extended; the error estimates are tighter and the information on the location of the solution is at least as precise as before. These advantages are obtained using the same information as before, since new Lipschitz constant are tighter and special cases of the ones used before. Numerical examples and applications are used to test favorable the theoretical results to earlier ones.

【 授权许可】

Unknown