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121121s2012 txu obm 000 0 eng d |
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|a (OCoLC)ocn818911509
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|a (OCoLC)818911509
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|a (TxCM)http://hdl.handle.net/1969.1/ETD-TAMU-2011-08-9967
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|a TXA
|c TXA
|d UtOrBLW
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|a TXAM
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|a 2011
|a Dissertation
|a 1969.1/ETD-TAMU-2011-08-9967
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|a Bailey, Benjamin Aaron.
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|a Studies in interpolation and approximation of multivariate bandlimited functions /
|c by Benjamin Aaron Bailey.
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|a [College Station, Tex.] :
|b [Texas A&M University],
|c [2012]
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|a 1 online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a "Major Subject: Mathematics"
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|a Description from author supplied metadata (automated record created 2012-10-22 13:24:58).
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|b Doctor of Philosophy
|c Texas A&M University
|d 2011
|o http://hdl.handle.net/1969.1/ETD-TAMU-2011-08-9967
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|a Includes bibliographical references.
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|a Text (Dissertation)
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|a The 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.
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|a Electronic resource.
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|a Major Mathematics.
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|a polynomial interpolation
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|a approximation
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|a bandlimited functions
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|a oversampling
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|a Schlumprecht, Thomas,
|e thesis advisor.
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|a Sivakumar, Natarajan,
|e thesis advisor.
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|u http://hdl.handle.net/1969.1/ETD-TAMU-2011-08-9967
|z Link to OAK Trust copy
|t 0
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| 948 |
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|a cataloged
|b h
|c 2012/11/21
|d o
|e jstorlie
|f 4:20:03 pm
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|a C0
|b TXA
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|a MARS
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|t 0
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| 952 |
f |
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|a Texas A&M University
|b College Station
|c Electronic Resources
|d Available Online
|t 0
|e 2011 Dissertation 1969.1/ETD-TAMU-2011-08-9967
|h Other scheme
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| 998 |
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|a 2011 Dissertation 1969.1/ETD-TAMU-2011-08-9967
|t 0
|l Available Online
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