• 论文 • 上一篇    下一篇

关于Kantorovich定理与Moore定理的等价性

沈祖和   

  1. 南京大学
  • 出版日期:1984-03-14 发布日期:1984-03-14

沈祖和. 关于Kantorovich定理与Moore定理的等价性[J]. 计算数学, 1984, 6(3): 319-323.

ON THE EQUIVALENCE OF THE EXISTENCE THEOREMS OF KANTOROVICH AND MOORE

  1. Shen Zu-he Nanjing University
  • Online:1984-03-14 Published:1984-03-14
Rall就Kantorovich定理与近年来新发展的关于区间迭代的Moore定理作了比较,指出前者在“敏感性”与“精确性”方面稍胜于后者,而在应用上后者所需要的计算量却少得多。本文证明这二个定理在理论上也是等价的。
A theoretical comparison by Rall shows that the Kantorovich theorem has at bestonly a slight edge in sensitivity and precision, while Moore's theorem requires far lesscomputation in application. The present paper demonstrates the theoretical equivalenceof these two theorems for nonlinear systems. That is, the Kantorovich condition h_0=η_0Kβ_0<1/2 is equivalent to the Moore test K(X) Int(X).
()

[1] W. B. Gragg, R. A. Tapia, Optimal error bounds for the Newton-Kantorovich theorem, SIAM J. Numer. Anal., 11 (1974) , 10-13.
[2] L. V. Kantorovich, Functional analysis and applied mathematics, Uspehi Mat. Nauk, 3 (1948) , 89-185.
[3] R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1966.
[4] R. E. Moore, A test for existence of solution to nonlinear system, SIAM J. Numer. Anal, 14(1971) , 611-615.
[5] R. E. Moore, A computational test for convergence of iterative methods for nonlinear systems, SIAM. J. Numer. Anal., 15 (1978) , 1194-1196.
[6] R. E. Moore, Methods and Applications of interval analysis, SIAM Publications, Philadelphia. 1979.
[7] L. B. Rall, A comparison of the existence theorems of Kantorovich and Moore, SIAM J. Numer. Anal., 17 (1980) , 148-161.
No related articles found!
阅读次数
全文


摘要