无穷维恒等算子的Kolmogorov n-宽度
Kolmogorov n-Width of Infinite Dimension Identity Operator
摘要: 本文讨论了无穷维恒等算子的Kolmogorov n-宽度,并计算了其精确渐近阶。
Abstract: In this paper, we study the Kolmogorov n-width of infinite dimension identity operator, and obtain its asymptotic degree.
文章引用:王桐心, 陆文静, 韩永杰, 梁柳. 无穷维恒等算子的Kolmogorov n-宽度[J]. 应用数学进展, 2018, 7(5): 519-524. https://doi.org/10.12677/AAM.2018.75063

参考文献

[1] Traub, J.F. Wasilkowski, G.W. and Wozniakowski, H. (1988) Information-Based Complexity. Academic Press, Boston, 1988.
[2] Kolmogorov, A.N. (1936) Uber die deste Annaherung yon funktionen einer gegebenen funktioneklasse. Annals of Mathematics, 37, 107-111. 〈br/〉 [Google Scholar] [CrossRef
[3] Stechkin, S.R. (1954) On Best Approximation of Given Classes of Functions by Arbitrary Polynomials. Uspekhi Matematicheskikh Nauk, 9, 133-134. (In Russian)
[4] Tikhomirov, V.M. (1960) Diameters of Sets in Function Spaces and the Theory of Best Approximations. Uspekhi Matematicheskikh Nauk, 15, 81-120.
[5] Pietsch, A. (1974) s-Numbers of Operators in Banach Spaces. Studia Mathematica, 51, 201-223. 〈br/〉 [Google Scholar] [CrossRef
[6] Stesin, M.I. (1975) Aleksandrov Widths of Finite—Dimensional Sets and Classes of Smooth Functions. Doklady Akademii Nauk, 220, 1278-1281.
[7] Ismagilov, R.S. (1974) Widths of Sets in Normed Linear Spaces and Approximation of Functions by Trigonometric Polynomials. Uspekhi Matematicheskikh Nauk, 29, 161-178.
[8] Pinkus, A. (1985) n-Widths in Approximation Theory. Springer, Berlin.