| 邱淑芳,王泽文,温荣生.稳定逼近Laplace算子与二阶混合偏导数的Lanczos方法[J].数学年刊A辑,2014,35(6):651~660 |
| 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 PartialDerivative of Second Order |
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| DOI： |
| 中文关键词: 不适定问题, 数值微分, Lanczos方法, 多元函数, 偏导数 |
| 英文关键词:Ill-posed problem, Numerical differentiation, Lanczos’ method,
Multivariate function, Partial derivative |
| 基金项目: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)和东华理工大学校长基金 (No.DHXK1208) |
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| 中文摘要: |
| 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$O(\delta^{\frac 12})$和$O(\delta^{\frac 23})$, 其中$\delta$是近似函数的误差水平. |
| 英文摘要: |
| 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(\delta^{\frac 12}) $ and $O(\delta^{\frac 23})$, where $\delta$ is the error
level of approximation of the unknown function. |
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