平均框架下线性张量积问题(s,t)-弱易处理性的两个结果
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摘要
<正>1引言用N表示正整数集合.对d∈N,设F_d为由d元函数组成的Banach空间,H_d为另一个Banach空间.每个映射S_d:F_d→H_d,d∈N被称为一个解算子.一个解算子序列S={S_d}_(d∈N)被称为一个多元问题.为求解这些解算子,我们常用信息基算法.本文中一个信息算子是指一个连续线性泛函.信息复杂度n(ε,d)指的是当我们用信息基算法逼近S_d:F_d→H_d时,为使得逼近误差小于ε所需要的连续线性泛函的最小数目.
In this paper we considered(s,t)-weak tractability of linear tensor product problems in the average case setting and improved our previous two results.
In this paper we considered(s,t)-weak tractability of linear tensor product problems in the average case setting and improved our previous two results.
引文
[1] Wozniakowski H. Tractability and strong tractability of linear multivariate problems. J. Complexity, 1994, 10:96-128.
[2] Novak E and Wozniakowski H. Tractability of Multivariate Problems. volume I:Linear Information. Berlin:EMS Tracts in Mathematics, 2008:6
[3] Novak E and Wozniakowski H. Tractability of Multivariate Problems. volume II:Standard Information for Functionals. Berlin:EMS Tracts in Mathematics, 2010:12
[4] Novak E and Wozniakowski H. Tractability of Multivariate Problems. volume III:Standard Information for Operators. Berlin:EMS Tracts in Mathematics, 2012:18
[5] Siedlecki P and Weimar M. Notes on(s,t)-weak tractability:A refined classification of problems with(sub)exponential information complexity. J Approx Theory, 2015, 200:227-258.
[6] Werschulz A G and Wozniakowski H. A new characterization of(s, t)-weak tractability. J.Complexity, 2017, 38:68-79.
[7] Siedlecki P.(s,t)-weak tractability of Euler and Wiener integrated processes. J Complexity,2016, 45:55-66.
[8] Chen J, Wang H and Zhang J. average case(s,t)-weak tractability of non-homogenous tensor product problems. J. Complexity, 2018, 49:27-45.
[9] Liu Y P and Xu G Q.(s, t)-weak tractability of multivariate linear problems in the average case setting. Acta Mathematica Sciential, 2019, 39(B):119-138.
[2] Novak E and Wozniakowski H. Tractability of Multivariate Problems. volume I:Linear Information. Berlin:EMS Tracts in Mathematics, 2008:6
[3] Novak E and Wozniakowski H. Tractability of Multivariate Problems. volume II:Standard Information for Functionals. Berlin:EMS Tracts in Mathematics, 2010:12
[4] Novak E and Wozniakowski H. Tractability of Multivariate Problems. volume III:Standard Information for Operators. Berlin:EMS Tracts in Mathematics, 2012:18
[5] Siedlecki P and Weimar M. Notes on(s,t)-weak tractability:A refined classification of problems with(sub)exponential information complexity. J Approx Theory, 2015, 200:227-258.
[6] Werschulz A G and Wozniakowski H. A new characterization of(s, t)-weak tractability. J.Complexity, 2017, 38:68-79.
[7] Siedlecki P.(s,t)-weak tractability of Euler and Wiener integrated processes. J Complexity,2016, 45:55-66.
[8] Chen J, Wang H and Zhang J. average case(s,t)-weak tractability of non-homogenous tensor product problems. J. Complexity, 2018, 49:27-45.
[9] Liu Y P and Xu G Q.(s, t)-weak tractability of multivariate linear problems in the average case setting. Acta Mathematica Sciential, 2019, 39(B):119-138.