PIECEWISE RATIONAL APPROXIMATIONS OF REAL ALGEBRAIC CURVES

作     者：Bajaj, CL Xu, GL 

作者机构：PURDUE UNIVDEPT COMP SCIW LAFAYETTEIN 47907 CHINESE ACAD SCISTATE KEY LAB SCI & ENGN COMPICMSECBEIJINGPEOPLES R CHINA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：1997年第15卷第1期

页      面：55-71页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：中国科学院项目 国家教育部项目 

主　　题：Math ACM PIECEWISE RATIONAL APPROXIMATIONS OF REAL ALGEBRAIC CURVES Design der 

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.