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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

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Showing 1 to 2 of 2 (0.139 seconds)

Spelling suggestions: "subject:"constrained least square approach""

1

On the Autoconvolution Equation and Total Variation Constraints

Fleischer, G., Gorenflo, R., Hofmann, B. 30 October 1998 (has links) (PDF)
This paper is concerned with the numerical analysis of the autoconvolution equation $x*x=y$ restricted to the interval [0,1]. We present a discrete constrained least squares approach and prove its convergence in $L^p(0,1),1<p<\infinite$ , where the regularization is based on a prescribed bound for the total variation of admissible solutions. This approach includes the case of non-smooth solutions possessing jumps. Moreover, an adaption to the Sobolev space $H^1(0,1)$ and some remarks on monotone functions are added. The paper is completed by a numerical case study concerning the determination of non-monotone smooth and non-smooth functions x from the autoconvolution equation with noisy data y.
autoconvolution
ill-posed problem
discretization
constrained least squares approach
bounded total variation
MSC 65J20
MSC 45G10
MSC 65R30
ddc:510
2

On the Autoconvolution Equation and Total Variation Constraints

Fleischer, G., Gorenflo, R., Hofmann, B. 30 October 1998 (has links)
This paper is concerned with the numerical analysis of the autoconvolution equation $x*x=y$ restricted to the interval [0,1]. We present a discrete constrained least squares approach and prove its convergence in $L^p(0,1),1<p<\infinite$ , where the regularization is based on a prescribed bound for the total variation of admissible solutions. This approach includes the case of non-smooth solutions possessing jumps. Moreover, an adaption to the Sobolev space $H^1(0,1)$ and some remarks on monotone functions are added. The paper is completed by a numerical case study concerning the determination of non-monotone smooth and non-smooth functions x from the autoconvolution equation with noisy data y.
info:eu-repo/classification/ddc/510
ddc:510
autoconvolution
ill-posed problem
discretization
constrained least squares approach
bounded total variation
MSC 65J20
MSC 45G10
MSC 65R30

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