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Hilbert Space Splittings and Iterative Methods

This book is about the theory of so-called Schwarz methods for solving variational problems in a Hilbert space V arising from linear equations and their associated quadratic minimization problems. Schwarz methods are based on the construction of a sequence of approximate solutions by solving auxilia...

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Sparad:
Bibliografiska uppgifter
Huvudupphovsmän: Griebel, Michael (Författare, medförfattare), Oswald, Peter (Författare, medförfattare)
Institutionell upphovsman: SpringerLink (Online service)
Materialtyp: Elektronisk E-bok
Språk:engelska
Publicerad: Cham : Springer Nature Switzerland : Imprint: Springer, 2024.
Upplaga:1st ed. 2024.
Serie:Springer Series in Computational Mathematics, 62
Ämnen:
Mathematics > Data processing.
Computational Mathematics and Numerical Analysis.
Länkar:https://doi.org/10.1007/978-3-031-74370-2
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Innehållsförteckning:
  • 1 Introduction
  • 2 Hilbert space splittings: Abstract theory
  • References
  • 3 Hilbert space splittings: Examples and extensions
  • References
  • 4 Schwarz iterative methods: Finite Omega
  • References
  • 5 Special topics and extensions
  • References
  • 6 Schwarz approximation methods: Infinite Omega
  • References
  • 7 Applications to PDE solvers
  • References
  • A Hilbert space basics
  • A.1 Spaces: Basic notation, definitions and properties
  • A.2 Operators between Hilbert spaces
  • A.3 Linear equations and variational problems
  • A.4 Constructions on Hilbert spaces
  • A.5 Sobolev spaces on domains
  • A.6 Reproducing kernel Hilbert spaces (RKHS)
  • References
  • Index.

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