Discrete p-bilaplacian Operators on Graphs

In this paper, we first introduce a new family of operators on weighted graphs called p-bilaplacian operators, which are the analogue on graphs of the continuous p-bilaplacian operators. We then turn to study regularized variational and boundary value problems associated to these operators. For inst...

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Autores principales: El Bouchairi, Imad, El Moataz, Abderrahim, Fadili, Jalal
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340938/
http://dx.doi.org/10.1007/978-3-030-51935-3_36
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author El Bouchairi, Imad
El Moataz, Abderrahim
Fadili, Jalal
author_facet El Bouchairi, Imad
El Moataz, Abderrahim
Fadili, Jalal
author_sort El Bouchairi, Imad
collection PubMed
description In this paper, we first introduce a new family of operators on weighted graphs called p-bilaplacian operators, which are the analogue on graphs of the continuous p-bilaplacian operators. We then turn to study regularized variational and boundary value problems associated to these operators. For instance, we study their well-posedness (existence and uniqueness). We also develop proximal splitting algorithms to solve these problems. We finally report numerical experiments to support our findings.
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spelling pubmed-73409382020-07-08 Discrete p-bilaplacian Operators on Graphs El Bouchairi, Imad El Moataz, Abderrahim Fadili, Jalal Image and Signal Processing Article In this paper, we first introduce a new family of operators on weighted graphs called p-bilaplacian operators, which are the analogue on graphs of the continuous p-bilaplacian operators. We then turn to study regularized variational and boundary value problems associated to these operators. For instance, we study their well-posedness (existence and uniqueness). We also develop proximal splitting algorithms to solve these problems. We finally report numerical experiments to support our findings. 2020-06-05 /pmc/articles/PMC7340938/ http://dx.doi.org/10.1007/978-3-030-51935-3_36 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
El Bouchairi, Imad
El Moataz, Abderrahim
Fadili, Jalal
Discrete p-bilaplacian Operators on Graphs
title Discrete p-bilaplacian Operators on Graphs
title_full Discrete p-bilaplacian Operators on Graphs
title_fullStr Discrete p-bilaplacian Operators on Graphs
title_full_unstemmed Discrete p-bilaplacian Operators on Graphs
title_short Discrete p-bilaplacian Operators on Graphs
title_sort discrete p-bilaplacian operators on graphs
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340938/
http://dx.doi.org/10.1007/978-3-030-51935-3_36
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AT fadilijalal discretepbilaplacianoperatorsongraphs

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