Studies in Interpolation and Approximation of Multivariate Bandlimited Functions

Simple item page
dc.contributorSchlumprecht, Thomas
dc.contributorSivakumar, Natarajan
dc.creatorBailey, Benjamin Aaron
dc.date.accessioned2012-10-19T15:29:08Z
dc.date.accessioned2012-10-22T18:06:05Z
dc.date.accessioned2017-04-07T20:02:07Z
dc.date.available2012-10-19T15:29:08Z
dc.date.available2012-10-22T18:06:05Z
dc.date.available2017-04-07T20:02:07Z
dc.date.created2011-08
dc.date.issued2012-10-19
dc.description.abstractThe focus of this dissertation is the interpolation and approximation of multivariate bandlimited functions via sampled (function) values. The first set of results investigates polynomial interpolation in connection with multivariate bandlimited functions. To this end, the concept of a uniformly invertible Riesz basis is developed (with examples), and is used to construct Lagrangian polynomial interpolants for particular classes of sampled square-summable data. These interpolants are used to derive two asymptotic recovery and approximation formulas. The first recovery formula is theoretically straightforward, with global convergence in the appropriate metrics; however, it becomes computationally complicated in the limit. This complexity is sidestepped in the second recovery formula, at the cost of requiring a more local form of convergence. The second set of results uses oversampling of data to establish a multivariate recovery formula. Under additional restrictions on the sampling sites and the frequency band, this formula demonstrates a certain stability with respect to sampling errors. Computational simplifications of this formula are also given.
dc.identifier.urihttp://hdl.handle.net/1969.1/ETD-TAMU-2011-08-9967
dc.language.isoen_US
dc.subjectbandlimited functions
dc.subjectpolynomial interpolation
dc.subjectapproximation
dc.subjectoversampling
dc.titleStudies in Interpolation and Approximation of Multivariate Bandlimited Functions
dc.typeThesis

Files

Collections

Texas A&M University at College Station