l_p空间上乘子函数类的最佳m-项单边逼近在Λ-Greedy算法下的收敛界  

The Convergent Bounds of the Best m-Term One-sided Approximation of the Multiplier Function Classes in l_p-Space for Λ-Greedy Algorithm

作　　者：李仁所[1] 孟宪勇[1] 

机构地区：[1]山东农业大学数学系,山东泰安271018

出　　处：《辽宁师范大学学报（自然科学版）》2006年第1期1-4,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10471010)

摘　　要：将在图像压缩、偏微分方程的近似解、统计分类等方面有着重要应用的非线性m-项逼近中的误差计算方法、Λ-Greedy逼近算法与广泛应用于运筹学、保形运算的单边逼近方法结合起来,给出了一种新的逼近方法—Λ-Greedy单边逼近.通过对由Fourier系数确定的乘子函数类由三角函数系给出的m-项单边逼近的性质的讨论,给出了此类乘子函数类的非线性m-项Λ-Greedy单边逼近算法及相应的类Greedy逼近算法在Lp范下的逼近上界的表达式.In this paper a new kind of approximation method, called non-linear m-term Λ-Greedy one-sided approximation, is introduced by combining the non linear m-term Λ-Greedy approximation which has applications in adaptive PDE solvers, compression of images and signal, statistical classification, and so on, with the one-sided approximation which has wide applications in conformal algorithm and operational research, etc. With this new kind of approximation method the bounds of non-linear m- term Λ-Greedy one-sided approximation determined by Fourier coefficients, and corresponding m- term Greedy-liked one-sided approximation results are given.

关 键 词：非线性最佳m-项逼近 Λ-Greedy逼近算法 单边逼近 Lp空间 三角函数 

分 类 号：O174.41[理学—数学]