关于不适定问题的迭代Tikhonov正则化方法
On the iterated Tikhonov regularization for ill-posed problems
查看参考文献7篇
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文摘
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讨论了求解不适定问题Kx=y的迭代Tikhonov正则化方法:x_α~0=0,(αI+K~*K)x_α~m=K~*y+αx_α~(m-1),m=1,2,…。文中将参数α取为固定常数(α>0),这时迭代次数m起到正则化参数的作用。推导出正则滤波函数的性质,给出正则化参数m的先验估计m=m(α,δ)=O(αδ~(-2/2r+1)),r≥0,证明了误差估计的收敛阶达到最优。在实际中,这种方法比将α看作正则化参数更容易计算。数值例子验证了理论结果。 |
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其他语种文摘
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The iterated Tikhonov regularization for solving ill-posed problems is considered:x_α~0=,(aI + K~* K)x_α~m= K~*y+αx_α~(m-1),m = 1,2,...The parameter m plays the role of the regularization parameter when the parameter a > 0 is fixed in this method.we deduce the property of regularizing filter function,give a priori optimal choice of m(a,δ)= O(aδ~(-2/2r+1)),r≥0 and obtain optimal order of convergence.In practice,it is more convenient than viewing a as the regularization parameter for computation.Finally,a numerical example is included to verify the theoretical results. |
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来源
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山东大学学报. 理学版
,2011,46(4):29-33 【核心库】
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关键词
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不适定问题
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迭代Tikhonov正则化
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先验估计
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收敛阶
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地址
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山东大学数学学院, 山东, 济南, 250100
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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1671-9352 |
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学科
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数学 |
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文献收藏号
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CSCD:4216544
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参考文献 共
7
共1页
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1.
KIRSCH A.
An introduction to the mathematical theory of inverse problems,1999
|
CSCD被引
8
次
|
|
|
|
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2.
SCHERZER O. Optimal a posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems.
SIAM J Numer Anal,1993,30(6):1796-1838
|
CSCD被引
8
次
|
|
|
|
|
3.
TAUTENHAHM U. The use of monotonicity for choosing the regularization parameter in ill-posed problems.
Inverse Problems,1999,15:1487-1505
|
CSCD被引
1
次
|
|
|
|
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4.
KING J T. Approximation of generalized inverses by iterated regularization.
Numer Funct Anal Optim,1979,1:499-513
|
CSCD被引
4
次
|
|
|
|
|
5.
ENGL H W. On the choice of the regularization parameter for iterated Tikhonov regularization of ill-posed problems.
J Approx Theory,1987,49:55-63
|
CSCD被引
5
次
|
|
|
|
|
6.
ENGL H W.
Regularization of inveres problems,1996
|
CSCD被引
1
次
|
|
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|
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7.
傅初黎. 不适定问题的迭代Tikhonov正则化方法.
计算数学,2006,28(3):237-245
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CSCD被引
13
次
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