Finite sections: A functional analytic perspective on approximation methods. Issue 3 (18th October 2018)

• Record Type: Journal Article
• Authors: Lindner, Marko; Seifert, Christian
• Other Names: Jacob Birgit guestEditor.; Behrndt Jussi guestEditor.; Tretter Christiane guestEditor.; Trunk Carsten guestEditor.
• Is Part Of: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik. Volume 41:Issue 3(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-10-18
• Subjects: applicability -- finite section method -- Galerkin method -- projection method -- stability; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; 510.5
• DOI: 10.1002/gamm.201800013
• Languages: English
• ISSNs: 0936-7195

Abstract

Abstract : We review approximation methods and their stability and applicability. We then focus on the finite section method and Galerkin methods and show that on separable Hilbert spaces either one can be interpreted as the other. In the end we demonstrate that well‐known methods such as the finite element method and polynomial chaos expansion are particular examples of the finite section method; their applicability can therefore be studied via the latter.