rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Newton’s Method: an Updated Approach of Kantorovich’s Theory
  name:
    name part: Ezquerro Fernández, José Antonio.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Hernández Verón, Miguel Ángel.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 166 p. 19 illus. in color. online resource.
  abstract: 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.
  table of contents: The classic theory of Kantorovich -- Convergence conditions on the second derivative of the operator -- Convergence conditions on the k-th derivative of the operator -- Convergence conditions on the first derivative of the operator.
  note: by José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón.
  subject:
    topic: Mathematics
  subject:
    topic: Integral equations
  subject:
    topic: Operator theory
  subject:
    topic: Computer mathematics
  subject:
    topic: Mathematics
  subject:
    topic: Operator Theory
  subject:
    topic: Computational Mathematics and Numerical Analysis
  subject:
    topic: Integral Equations
  classification: QA329-329.9
  classification: 515.724
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Frontiers in Mathematics
  identifier: 9783319559766
  identifier: http://dx.doi.org/10.1007/978-3-319-55976-6
  record info:
    record creation date: 170706
    record change date: 20170706120450.0
    record identifier: 978-3-319-55976-6