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Wavelet based numerical methods.

Shen, Xiaoping.

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Wavelet based numerical methods.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Wavelet based numerical methods./
Author:	Shen, Xiaoping.
Description:	150 p.
Notes:	Source: Dissertation Abstracts International, Volume: 58-07, Section: B, page: 3679.
Contained By:	Dissertation Abstracts International58-07B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9738680
ISBN:	0591503344

Wavelet based numerical methods.
Shen, Xiaoping.

Wavelet based numerical methods. - 150 p.

Source: Dissertation Abstracts International, Volume: 58-07, Section: B, page: 3679.

Thesis (Ph.D.)--The University of Wisconsin - Milwaukee, 1997.

Wavelet Analysis has developed rapidly in the past 15 years--for both theoretical and practical purposes. In this thesis, we focus on developing wavelet based numerical methods. The subjects include: (1) Positive estimation with wavelets, which is devoted to the discussion of the so call Gibbs' phenomenon arising in the wavelet expansions. (2) Quadrature formula based on sampling in Meyer wavelet subspaces. A weighted sampling type formula is established and the convergence and error bounds are obtained. (3) Galerkin-wavelet method for a singular convolution equation of first kind. The raised-cosine wavelets are used as the basis. The results related to convergence rate and error bounds are discussed. (4) Deconvolution using Meyer wavelets. An approach to deconvolution is introduced in which 'ill-posed' problem is converted to a well posed problem in both scaling and wavelet subspaces. Two cases, namely, when kernel has a non vanishing Fourier transform or when the kernel possesses a zero at origin are treated separately.

ISBN: 0591503344Subjects--Topical Terms:

515831
Mathematics.

Wavelet based numerical methods.
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100 1 $a Shen, Xiaoping. $3 700223
245 1 0 $a Wavelet based numerical methods.
300 $a 150 p.
500 $a Source: Dissertation Abstracts International, Volume: 58-07, Section: B, page: 3679.
500 $a Supervisor: Gilbert G. Walter.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Milwaukee, 1997.
520 $a Wavelet Analysis has developed rapidly in the past 15 years--for both theoretical and practical purposes. In this thesis, we focus on developing wavelet based numerical methods. The subjects include: (1) Positive estimation with wavelets, which is devoted to the discussion of the so call Gibbs' phenomenon arising in the wavelet expansions. (2) Quadrature formula based on sampling in Meyer wavelet subspaces. A weighted sampling type formula is established and the convergence and error bounds are obtained. (3) Galerkin-wavelet method for a singular convolution equation of first kind. The raised-cosine wavelets are used as the basis. The results related to convergence rate and error bounds are discussed. (4) Deconvolution using Meyer wavelets. An approach to deconvolution is introduced in which 'ill-posed' problem is converted to a well posed problem in both scaling and wavelet subspaces. Two cases, namely, when kernel has a non vanishing Fourier transform or when the kernel possesses a zero at origin are treated separately.
520 $a Numerical examples are given to illustrate the theoretical results.
590 $a School code: 0263.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a The University of Wisconsin - Milwaukee. $3 1019345
773 0 $t Dissertation Abstracts International $g 58-07B.
790 1 0 $a Walter, Gilbert G., $e advisor
790 $a 0263
791 $a Ph.D.
792 $a 1997
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9738680