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121128s2012 txu obm 000 0 eng d |
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|a (OCoLC)ocn819532635
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|a (OCoLC)819532635
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|a (TxCM)http://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8404
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|a TXA
|c TXA
|d UtOrBLW
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|a TXAM
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|a 2010
|a Dissertation
|a 1969.1/ETD-TAMU-2010-08-8404
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|a Ward, John Paul.
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|a L^p bernstein inequalities and radial basis function approximation /
|c by John Paul Ward.
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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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| 502 |
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|b Doctor of Philosophy
|c Texas A&M University
|d 2010
|o http://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8404
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|a Includes bibliographical references.
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|a Text (Dissertation)
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|a In approximation theory, three classical types of results are direct theorems, Bernstein inequalities, and inverse theorems. In this paper, we include results about radial basis function (RBF) approximation from all three classes. Bernstein inequalities are a recent development in the theory of RBF approximation, and on Rd, only L2 results are known for RBFs with algebraically decaying Fourier transforms (e.g. the Sobolev splines and thin-plate splines). We will therefore extend what is known by establishing Lp Bernstein inequalities for RBF networks on Rd. These inequalities involve bounding a Bessel-potential norm of an RBF network by its corresponding Lp norm in terms of the separation radius associated with the network. While Bernstein inequalities have a variety of applications in approximation theory, they are most commonly used to prove inverse theorems. Therefore, using the Lp Bernstein inequalities for RBF approximants, we will establish the corresponding inverse theorems. The direct theorems of this paper relate to approximation in Lp(Rd) by RBFs which are perturbations of Green's functions. Results of this type are known for certain compact domains, and results have recently been derived for approximation in Lp(Rd) by RBFs that are Green's functions. Therefore, we will prove that known results for approximation in Lp(Rd) hold for a larger class of RBFs. We will then show how this result can be used to derive rates for approximation by Wendland functions.
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|a Electronic resource.
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|a Major Mathematics.
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|a Bernstein inequalities
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|a radial basis functions
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|a Narcowich, Francis J.,
|e thesis advisor.
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| 700 |
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|a Ward, J. D.
|q (Joseph D.),
|e thesis advisor.
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|u http://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8404
|z Link to OAK Trust copy
|t 0
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| 952 |
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|a Texas A&M University
|b College Station
|c Electronic Resources
|d Available Online
|t 0
|e 2010 Dissertation 1969.1/ETD-TAMU-2010-08-8404
|h Other scheme
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| 998 |
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|a 2010 Dissertation 1969.1/ETD-TAMU-2010-08-8404
|t 0
|l Available Online
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