{"title":"de casteljau型算法和Bernstein表示的准确性","authors":"J. Delgado, E. Mainar, J.M. Peña","doi":"10.1016/j.cagd.2023.102243","DOIUrl":null,"url":null,"abstract":"<div><p>This paper summarizes interesting results on systematic backward and forward error analyses performed for corner cutting algorithms providing evaluation of univariate and multivariate functions defined in terms of Bernstein and Bernstein related bases. Relevant results on the conditioning of the bases are also recalled. Finally, the paper surveys important advances, lately obtained, for the design of algorithms adapted to the structure of totally positive matrices, allowing the resolution of interpolation and approximation problems with Bernstein-type bases achieving computations to high relative accuracy.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"106 ","pages":"Article 102243"},"PeriodicalIF":1.3000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the accuracy of de Casteljau-type algorithms and Bernstein representations\",\"authors\":\"J. Delgado, E. Mainar, J.M. Peña\",\"doi\":\"10.1016/j.cagd.2023.102243\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper summarizes interesting results on systematic backward and forward error analyses performed for corner cutting algorithms providing evaluation of univariate and multivariate functions defined in terms of Bernstein and Bernstein related bases. Relevant results on the conditioning of the bases are also recalled. Finally, the paper surveys important advances, lately obtained, for the design of algorithms adapted to the structure of totally positive matrices, allowing the resolution of interpolation and approximation problems with Bernstein-type bases achieving computations to high relative accuracy.</p></div>\",\"PeriodicalId\":55226,\"journal\":{\"name\":\"Computer Aided Geometric Design\",\"volume\":\"106 \",\"pages\":\"Article 102243\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Aided Geometric Design\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167839623000754\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Aided Geometric Design","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167839623000754","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
On the accuracy of de Casteljau-type algorithms and Bernstein representations
This paper summarizes interesting results on systematic backward and forward error analyses performed for corner cutting algorithms providing evaluation of univariate and multivariate functions defined in terms of Bernstein and Bernstein related bases. Relevant results on the conditioning of the bases are also recalled. Finally, the paper surveys important advances, lately obtained, for the design of algorithms adapted to the structure of totally positive matrices, allowing the resolution of interpolation and approximation problems with Bernstein-type bases achieving computations to high relative accuracy.
期刊介绍：
The journal Computer Aided Geometric Design is for researchers, scholars, and software developers dealing with mathematical and computational methods for the description of geometric objects as they arise in areas ranging from CAD/CAM to robotics and scientific visualization. The journal publishes original research papers, survey papers and with quick editorial decisions short communications of at most 3 pages. The primary objects of interest are curves, surfaces, and volumes such as splines (NURBS), meshes, subdivision surfaces as well as algorithms to generate, analyze, and manipulate them. This journal will report on new developments in CAGD and its applications, including but not restricted to the following:
-Mathematical and Geometric Foundations-
Curve, Surface, and Volume generation-
CAGD applications in Numerical Analysis, Computational Geometry, Computer Graphics, or Computer Vision-
Industrial, medical, and scientific applications.
The aim is to collect and disseminate information on computer aided design in one journal. To provide the user community with methods and algorithms for representing curves and surfaces. To illustrate computer aided geometric design by means of interesting applications. To combine curve and surface methods with computer graphics. To explain scientific phenomena by means of computer graphics. To concentrate on the interaction between theory and application. To expose unsolved problems of the practice. To develop new methods in computer aided geometry.
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