Pub Date : 2021-02-19DOI: 10.1007/S40314-021-01425-6
Z. Hebbache, K. Guenda, N. T. Özzaim, Mehmet Ozen, T. Gulliver
{"title":"Some skew constacyclic codes over $$mathbb {F}_{q}+umathbb {F}_{q}$$","authors":"Z. Hebbache, K. Guenda, N. T. Özzaim, Mehmet Ozen, T. Gulliver","doi":"10.1007/S40314-021-01425-6","DOIUrl":"https://doi.org/10.1007/S40314-021-01425-6","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86660236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-08DOI: 10.1007/S40314-020-01388-0
Jian Tang, N. Yaqoob
{"title":"A novel investigation on fuzzy hyperideals in ordered $$*$$-semihypergroups","authors":"Jian Tang, N. Yaqoob","doi":"10.1007/S40314-020-01388-0","DOIUrl":"https://doi.org/10.1007/S40314-020-01388-0","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89655773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.
{"title":"An optimization-based approach to parameter learning for fractional type nonlocal models","authors":"O. Burkovska, Christian A. Glusa, M. D'Elia","doi":"10.2172/1673822","DOIUrl":"https://doi.org/10.2172/1673822","url":null,"abstract":"Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74110800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove for the first time convergence of a stochastic collocation algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.
{"title":"Convergence of adaptive stochastic collocation with finite elements","authors":"M. Feischl, Andrea Scaglioni","doi":"10.5445/IR/1000125783","DOIUrl":"https://doi.org/10.5445/IR/1000125783","url":null,"abstract":"We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove for the first time convergence of a stochastic collocation algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78732560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-27DOI: 10.1007/s40314-020-01304-6
J. Sousa, G. Frederico, E. C. de Oliveira
{"title":"$$psi $$-Hilfer pseudo-fractional operator: new results about fractional calculus","authors":"J. Sousa, G. Frederico, E. C. de Oliveira","doi":"10.1007/s40314-020-01304-6","DOIUrl":"https://doi.org/10.1007/s40314-020-01304-6","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85864844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-08DOI: 10.1007/s40314-020-01194-8
Lu-Bin Cui, Xiao-Qing Zhang, Shiliang Wu
{"title":"A new preconditioner of the tensor splitting iterative method for solving multi-linear systems with $$mathcal {M}$$-tensors","authors":"Lu-Bin Cui, Xiao-Qing Zhang, Shiliang Wu","doi":"10.1007/s40314-020-01194-8","DOIUrl":"https://doi.org/10.1007/s40314-020-01194-8","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78607338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1007/s40314-020-01174-y
Rizwana Gul, M. Shabir
{"title":"Roughness of a set by $$(alpha , beta )$$-indiscernibility of Bipolar fuzzy relation","authors":"Rizwana Gul, M. Shabir","doi":"10.1007/s40314-020-01174-y","DOIUrl":"https://doi.org/10.1007/s40314-020-01174-y","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79853440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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