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本文讨论了变阶可解逼近族的插值逼近和带权逼近(权在插值点集Z上趋于无穷而在Z外为1)的关系.指出对变阶可解族而言,当逼近解为非亏损时,稠密性假设是自然满足的,且此时的最佳插值逼近等于该带权最佳逼近的极限.  相似文献   
2.
In this note,we develop,without assuming the Haar condition,a generalized simultaneousChebyshev approximation theory which is similar to the classical Chebyshev theory and con-rains it as a special case.Our results also contain those in[1]and[3]as a special case,and thetwo conjectures proposed by C.B.Dunham in[2]are proved to be true in the case of simulta-neous approximation.  相似文献   
3.
In this note, the author discusses the problem of best simultaneous approximation by function pairs. The existence and characterization theorems of the best simultaneous approximation in L1 and L norms are obtained respectively, and some rezults of [ 1 ] are the special case of the theorems of the paper.  相似文献   
4.
1PreliminariesandExistenceForfEC[0,1],A.PinkusandO.Shi.h.[l]introducedthefollowingmeasures,'Thesupremaareattainable,andqE[1,co)Inthecaseq=1,wesimplyletWiththismeasurestA.PinkusandO.ShishahavestudiedbestapproximationbyalgebraicpolynondaISofdegree5n.Later,MaandShi[2]11avestudiedthecaseofbestapproximationfromratiollalpolyllollilalsR:,usingthesamegaugeill'JI1.TheyallgetthesimilarresultsforChebyshevapproximation,includingalternatiolltheoremascharacterisatiollforthebestappro~swhichisthegeom…  相似文献   
5.
罗祖华  陈业华 《数学杂志》1993,13(2):221-228
本文在不假定 G 在紧集 X 上满足 Haar 条件的情形,建立了 Dunham 型联合最佳逼近的 Chebyshev 理论,包括特征定理(定理5、定理6和推论2),唯一性与强唯一性定理(定理9和推论3)以及连续性定理,同时我们也得到了“削皮”定理与联合最佳逼近的量的对偶形式。(定理7)。  相似文献   
6.
Let X={x_0,x_1…,x_n}and let c(X)be the set of all continuous real functions on X with the Chebyshev norm. Let G=span{g_1,g_2,…,g_n}be an n-dimensional subspace of c(X).Let T={(f~+,f~-):f~+≥f~-and f~+,f~-∈c(X)}.If there exists a P∈G such that max{||f~+-P||, ||f~--P||}=inf{max{||f~+-Q||, ||f~--Q||}:Q∈G},(1) then P is called a best simultaneous approximation to(f~+,f~-)from G.  相似文献   
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