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关于非线性切比雪夫逼近的几点注记

何新贵   

  • 出版日期:1983-02-14 发布日期:1983-02-14

何新贵. 关于非线性切比雪夫逼近的几点注记[J]. 计算数学, 1983, 5(2): 204-207.

SOME NOTES ON NON-LINEAR TCHEBYCHEFF APPROXIMATION

  1. He Xin-gui
  • Online:1983-02-14 Published:1983-02-14
本文讨论了一类非线性切比雪夫逼近问题的两个具体算法,证明了它们的收敛性.实际计算表明,效果很好. 设f(x)与F(A,x)为给定的两个实连续函数,其中x∈M,A=(a_1,a_2,…,a_n)∈?,M表示实轴上的某个有界闭集,?是n维欧氏空间中的子集.切比雪夫逼近问题就是在?中确定A~*∈?,使对一切A∈?,有
Two iterative algorithms on non-linear Tchebycheff approximation are discussedand their convergence is proved. The algorithm is very efficient in practice of computa-tion.
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[1] E. L. Stiefel, Numerical methods of Tebycheff approximation, On numerical approximation, 217-232.
[2] E. 44--47, 1957.
[3] T. S. Motzkin, Approximation by curves of a unisolvent family, Bull. Amer. Math. Soc., 55, 789-793.
[4] L. T. Tornkeim, On n-parameter family of functions and associated conven functions, Trans. Amer. Math. Soc., 69, 457--467.
[5] 阿赫叶惹尔,逼近论讲义,1957.
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