RATIONAL CHEBYSHEV APPROXIMATION WITH VARIOUS DENOMINATOR CONSTRAINTS

作     者：CharlesB.Dunham 

作者机构：Computer Science Department University of Western Ontario London Ontario N6A 5B7 CANADA 

出 版 物：《Analysis in Theory and Applications》 (分析,理论与应用(英文版))

年 卷 期：1986年第4期

页      面：1-19页

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

主　　题：RATIONAL CHEBYSHEV APPROXIMATION WITH VARIOUS DENOMINATOR CONSTRAINTS 

摘      要：Chebyshev approximation by families of generalized rationalfunctions is considered, with various inequality constraints ondenominators being studied. The classical family of rationals R;with denominator0 is reviewed. Next the family of rationals R;with non-vanishing denominator is *** absence of a charac-terization or uniqueness result is shown. To help in the analysisof R;, the elass of families R;（s） is introduced, where s is a non-zero sign function and denominators take sign s. Such families areshown to have a theory equivalent to that for R;A difficultywith the families R;, R;, R;（s） is that a best approximation may notexist and analytical processes may not have a limit. To remedythis defioiency we add rationals whose denominators have zeros toget the families R;, R, R;（s） respectively. Conventions of Boehmand Goldstein for evaluation at zeros are reviewed. Under statedconditions, existence is guaranteed. Unfortunately, neither astandard characterization nor uniqueness need hold for these largerfamilies. Further, such additions may change the distance fromfunction to approximating family. When a best approximation fromR;is also best in R;is studied. Uniqueness of best approxima-tions from R;, R;（s）, and R;is studied. Existence of best appro-ximations by R;and R;is studied.