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Multivariate Polynomial Interpolation and the Lifting Scheme with an Application to Scattered Data Approximation

  • This thesis deals with generalized inverses, multivariate polynomial interpolation and approximation of scattered data. Moreover, it covers the lifting scheme, which basically links the aforementioned topics. For instance, determining filters for the lifting scheme is connected to multivariate polynomial interpolation. More precisely, sets of interpolation sites are required that can be interpolated by a unique polynomial of a certain degree. In this thesis a new class of such sets is introduced and elements from this class are used to construct new and computationally more efficient filters for the lifting scheme. Furthermore, a method to approximate multidimensional scattered data is introduced which is based on the lifting scheme. A major task in this method is to solve an ordinary linear least squares problem which possesses a special structure. Exploiting this structure yields better approximations and therefore this particular least squares problem is analyzed in detail. This leads to a characterization of special generalized inverses with partially prescribed image spaces.

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Author:Dominik Stahl
URN (permanent link):urn:nbn:de:hbz:386-kluedo-35664
Advisor:Tobias Damm
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2013/07/10
Year of Publication:2013
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2013/04/17
Date of the Publication (Server):2013/07/10
Number of page:108
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012