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Energy Blowup of Sampling-based Approximation Methods

Abstract: 

This work considers the problem of approximating continuous functions of finite Dirichlet energy from samples of these functions. It will be shown that there exists no sampling-based method which is able to approximate every function in this space from its samples. Specifically, we show that for any sampling based approximation method, the energy of the approximation tends to infinity as the number of samples is increased for almost every continuous function of finite energy. As an application, we study the problem of solving the Dirichlet problem on a bounded region. It is shown that if only samples of the boundary function can be processed then the energy of the solution can not be controlled for any function from a non-meager dense set.

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Paper Details

Authors:
Holger Boche, Volker Pohl
Submitted On:
10 May 2019 - 7:36am
Short Link:
Type:
Poster
Event:
Presenter's Name:
Volker Pohl
Paper Code:
1866
Document Year:
2019
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Document Files

BochePohl_ICASSP19.pdf

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[1] Holger Boche, Volker Pohl, "Energy Blowup of Sampling-based Approximation Methods", IEEE SigPort, 2019. [Online]. Available: http://sigport.org/4307. Accessed: Oct. 24, 2020.
@article{4307-19,
url = {http://sigport.org/4307},
author = {Holger Boche; Volker Pohl },
publisher = {IEEE SigPort},
title = {Energy Blowup of Sampling-based Approximation Methods},
year = {2019} }
TY - EJOUR
T1 - Energy Blowup of Sampling-based Approximation Methods
AU - Holger Boche; Volker Pohl
PY - 2019
PB - IEEE SigPort
UR - http://sigport.org/4307
ER -
Holger Boche, Volker Pohl. (2019). Energy Blowup of Sampling-based Approximation Methods. IEEE SigPort. http://sigport.org/4307
Holger Boche, Volker Pohl, 2019. Energy Blowup of Sampling-based Approximation Methods. Available at: http://sigport.org/4307.
Holger Boche, Volker Pohl. (2019). "Energy Blowup of Sampling-based Approximation Methods." Web.
1. Holger Boche, Volker Pohl. Energy Blowup of Sampling-based Approximation Methods [Internet]. IEEE SigPort; 2019. Available from : http://sigport.org/4307