稳定逼近Laplace算子与二阶混合偏导数的Lanczos方法  

Lanczos' Methods for Stably Approximating Laplace Operator and Mixed Partial Derivative of Second Order

作　　者：邱淑芳[1] 王泽文[1] 温荣生[1] 

机构地区：[1]东华理工大学理学院,南昌330013

出　　处：《数学年刊（A辑）》2014年第6期651-660,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11161002);江西省青年科学家培养计划(No.20122BCB23024);江西省自然科学基金(No.2010GZS0010);东华理工大学校长基金(No.DHXK1208)的资助

摘　　要：考虑由未知二元函数的近似值计算其Laplace算子与二阶混合偏导数的问题,给出稳定逼近Laplace算子与二阶混合偏导数的两类Lanczos方法,其逼近精度分别为O(δ^(1/2))和O(δ^(2/3)),其中δ是近似函数的误差水平.The ill-posed problem to numerically calculating the Laplace operator and the mixed partial derivative of second order of an unknown function from its noise data is considered in this paper.Two kinds of Lanczos' methods are proposed to stably approximate the Laplace operator and the mixed partial derivative of second order,and their convergence rates are respectively O(δ^(1/2)) and O(δ^(2/3)),where δ is the error level of approximation of the unknown function.

关 键 词：不适定问题 数值微分 LANCZOS方法 多元函数 偏导数 

分 类 号：O177[理学—数学]