• 论文 • 上一篇    下一篇

Dunham型联合最佳逼近

史应光   

  1. 中国科学院计算中心
  • 出版日期:1981-03-20 发布日期:1981-03-20

史应光. Dunham型联合最佳逼近[J]. 数值计算与计算机应用, 1981, 2(3): 138-142.

ON THE SIMULTANEOUSLY BEST APPROXIMATION FOR DUNHAM-TYPE

  1. Shih Ying-kuang Computing Center, Academia Sinica
  • Online:1981-03-20 Published:1981-03-20
设X[a,b]为紧集,对X上的任意实值函数f,定义||f||=sup|f(x)|.又设MC[a,b]为n维Haar子空间,{φ_1,…,φ_n}为它的任一基底,其中n是自然数.Dunham在中提出了下述联合最佳逼近问题.设f~+和-f~-是X上的上半连续函数,而且f~+≥f~-(为了方便,我们将这样的函数偶(f~+,f~-)的全体记作),寻找一个P∈M(这里我们不用非线性的n阶唯一可解函数,而用M中的元素作逼近函数)使它满足
In this paper, we discuss the problem of simultaneously best approximation forDunham-type, i.e. one of minimization of the functional φ(P) = max {||f~+ - P||,||f~- - P||}. We have given a characterization theorem and proved a strong uniguenesstheorem and a continuity one. Finally, we have provided an algorithm for calculatingthe best approximation.
()

[1] C. B. Dunham, Simultaneous chedyshev approximation of function on ax interval, Proc. Amer. Math. Soc., 18: 3(1967) , 472-477.
[2] J. B. Diaz, H. W. McLaughlin. Simultaneous approximation of a set of bounded real functions, Math. Comp., 23: 107(1969) , 583-594.
[3] J. B. Diaz, H. W. Mclaughlin, On simultaneous Chebyshev approximation and Chebyshev approximation with an additive weight, J. Approx. Theory, 6: 1 (1972) , 68-71.
[4] E. W. Cheney, Introduction to approximation theory, McGraw-Hill, New York, 1966.
No related articles found!
阅读次数
全文


摘要