| 周期函数的数值微分问题 |
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| 引用本文： | 杨古帆,叶予璋,王盛章.周期函数的数值微分问题[J].复旦学报(自然科学版),2004,43(3):315-322. |
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| 作者姓名： | 杨古帆 叶予璋 王盛章 |
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| 作者单位： | 复旦大学,数学研究所,上海,200433;北海道大学,数学系,日本扎幌,060-0810 |
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| 摘 要： | 用Tikhonov正则化方法讨论了周期函数的数值微分问题．证明Tikhonov正则化泛函存在唯一的极小元，且这个极小元是一个周期样条，并给出了该方法的误差估计．同其他相关的工作相比，发现对周期函数而言，此方法在边界上拟合的效果更好．
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| 关 键 词： | 不适定问题 Tikhonov正则化方法 数值微分 变分法 周期样条 |
| 文章编号： | 0427-7104(2004)03-0315-08 |
Numerical Differentiation for Periodic Functionsand Its Applications |
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| YANG Gu-fan.Numerical Differentiation for Periodic Functionsand Its Applications[J].Journal of Fudan University(Natural Science),2004,43(3):315-322. |
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| Authors: | YANG Gu-fan |
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| Institution: | YANG Gu-fan~ |
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| Abstract: | The numerical differentiation for the periodic functions is discussed by Tikhonov redularization. It is shown that there exists a unique minimizer for the Tikhonov regularization functional and minimizer is a periodic spline. The error estimate of our method is also given. Compared with other related methods, it gives better approximation on the boundary points. one numerical example is presented . |
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| Keywords: | ill-posed problems Tikhonov regularization numerical differentiation variation periodic spline |
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