积分算子的n-逼近数

黄正达

数学学报 ›› 1994, Vol. 37 ›› Issue (3) : 338-348.

数学学报 ›› 1994, Vol. 37 ›› Issue (3) : 338-348. DOI: 10.12386/A1994sxxb0044
论文

积分算子的n-逼近数

    黄正达
作者信息 +

n-Approximation Number of Integral Operator

Author information +
文章历史 +

摘要

本文研究了积分算子TK:Lq[0,1]→Lq[0,1],(q≥1)当核 K(s, t)是 Sobolev空间 Wpr([0, 1]2)中元素时n-逼近数 an(TK: Lq→ Lq)的估计,并把这个估计应用于退化核方法解第二类线性Fredholm方程(I一TK)x=y时,Badhvalov[5]意义下最佳误差的讨论中,所得到的最佳误差之估计当q=1时,最优化了[10]的结论.

Abstract

This paper is concerned with the study of the error estimate of n-approximation number an (Tk: Lq ~ Lq), where Tk : Lq[0, 1] - Lq[0, 1] (q >=1), (TK)(s) = 1 0 K(s,t)x(t)dt, s E [0, 1], and kernal K(s, t) E W p r ([0, 1]2). When the result of study is applied to optimal error estimate (Bakhvalov [5]) of solving the second linear Fredholm equation (I - TK)x - y using degenerate method, it produces an optimal error estimate which optimizes that in [10] when q = 1.

关键词

最佳误差估计 / n-逼近数 / 退化核方法

引用本文

导出引用
黄正达. 积分算子的n-逼近数. 数学学报, 1994, 37(3): 338-348 https://doi.org/10.12386/A1994sxxb0044
n-Approximation Number of Integral Operator. Acta Mathematica Sinica, Chinese Series, 1994, 37(3): 338-348 https://doi.org/10.12386/A1994sxxb0044

Accesses

Citation

Detail

段落导航
相关文章

/