书目名称 | Newton’s Method: an Updated Approach of Kantorovich’s Theory |
编辑 | José Antonio Ezquerro Fernández,Miguel Ángel Herná |
视频video | |
概述 | Up-to-date account of Kantorovich´s theory for Newton´s method.Starts with a detailed presentation of Kantorovich´s approach and ends with new results and alternative approaches.Contains many numerica |
丛书名称 | Frontiers in Mathematics |
图书封面 |  |
描述 | .This book shows the importance of studying semilocal convergence in iterative methods through Newton‘s method and addresses the most important aspects of the Kantorovich‘s theory including implicated studies. Kantorovich‘s theory for Newton‘s method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich‘s theory for Newton‘s method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton‘s method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular.. |
出版日期 | Book 2017 |
关键词 | Newton’s Method; Kantorovich’s Theory; Semilocal Convergence; Majorizing Sequence; Error Estimates; Order |
版次 | 1 |
doi | https://doi.org/10.1007/978-3-319-55976-6 |
isbn_softcover | 978-3-319-55975-9 |
isbn_ebook | 978-3-319-55976-6Series ISSN 1660-8046 Series E-ISSN 1660-8054 |
issn_series | 1660-8046 |
copyright | Springer International Publishing AG 2017 |