"A visual and numerical comparative study of some parallel affine projection algorithms for solving the convex feasibility problem with application to scratch inpainting"
{"title":"\"A visual and numerical comparative study of some parallel affine projection algorithms for solving the convex feasibility problem with application to scratch inpainting\"","authors":"Irina Maria Artinescu, C. Boldea","doi":"10.37193/cjm.2022.02.03","DOIUrl":null,"url":null,"abstract":"\"The paper compares four variants of algorithms that solve the problem of Convex Feasibility using affine combinations of projections, two classical variants of Parallel Projection Method (PPM) and two modified variants that involve variable weight, in terms of their effectiveness in inpainting a convex polygon, as well as in terms of their convergence in a finite a number of step. We also present a numerical study of the dependence of the efficiency and the execution speed of these algorithms on the shape of the inpainted convex set, as well as on the values of the relaxation parameter.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Carpathian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.37193/cjm.2022.02.03","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
"The paper compares four variants of algorithms that solve the problem of Convex Feasibility using affine combinations of projections, two classical variants of Parallel Projection Method (PPM) and two modified variants that involve variable weight, in terms of their effectiveness in inpainting a convex polygon, as well as in terms of their convergence in a finite a number of step. We also present a numerical study of the dependence of the efficiency and the execution speed of these algorithms on the shape of the inpainted convex set, as well as on the values of the relaxation parameter."
期刊介绍:
Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.