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
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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
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脚注
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