Piecewise rational approximations of real algebraic curves

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	Piecewise rational approximations of real algebraic curves
	Bajaj, CL ; Xu, GL
	1997
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	15 期号:1 页码:55-71
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.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:A1997WD52300005
出版者	VSP BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/28956
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.