Piecewise rational approximations of real algebraic curves
文献类型：期刊论文
| 作者 | Bajaj, CL; Xu, GL |
| 刊名 | JOURNAL OF COMPUTATIONAL MATHEMATICS
 |
| 出版日期 | 1997 |
| 卷号 | 15期号:1页码:55-71 |
| ISSN号 | 0254-9409 |
| 英文摘要 | We use a combination of both algebraic and numerical techniques to construct a C-1-continuous, piecewise (m, n) rational epsilon-approximation of a real algebraic plane curve of degree d. At singular points we use the classical Weierstrass Preparation Theorem and Newton power series factorizations, based on the technique of Hensel lifting. These, together with modified rational Pade approximations, are used to efficiently construct locally approximate, rational parametric representations for all real branches of an algebraic plane curve. Besides singular points we obtain an adaptive selection of simple points about which the curve approximations yield a small number of pieces yet achieve C-1 continuity between pieces. The simpler cases of C-1 and C-0 continuity are also handled in a similar manner. The computation of singularity, the approximation error bounds and details of the implementation of these algorithms are also provided. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:A1997WD52300005 |
| 出版者 | VSP BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/28955]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 作者单位 | 1.PURDUE UNIV,DEPT COMP SCI,W LAFAYETTE,IN 47907 2.CHINESE ACAD SCI,STATE KEY LAB SCI & ENGN COMP,ICMSEC,BEIJING,PEOPLES R CHINA |
| 推荐引用方式 GB/T 7714 | Bajaj, CL,Xu, GL. Piecewise rational approximations of real algebraic curves[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,1997,15(1):55-71. |
| APA | Bajaj, CL,&Xu, GL.(1997).Piecewise rational approximations of real algebraic curves.JOURNAL OF COMPUTATIONAL MATHEMATICS,15(1),55-71. |
| MLA | Bajaj, CL,et al."Piecewise rational approximations of real algebraic curves".JOURNAL OF COMPUTATIONAL MATHEMATICS 15.1(1997):55-71. |
入库方式： OAI收割
来源：数学与系统科学研究院
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