| 求解大规模线性离散不适定反问题的修正LSQR算法及其杂交型算法 |
| Alternative Title | A Modified LSQR Algorithm and Its Hybrid Algorithm for Solving Large-Scale Linear Discrete Ill-Posed Inverse Problems
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| 郑大威 |
| Thesis Advisor | 郑兵
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| 2011-05-28
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| Degree Grantor | 兰州大学
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| Place of Conferral | 兰州
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| Degree Name | 硕士
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| Keyword | 不适定问题
LSQR
正则化
Tikhonov
Lanczos算法
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| Abstract | 不适定反问题在当今众多的科学领域中都有着广泛的应用，经典的正则化方法是针对这类问题设定的计算平稳解的有效方法和手段。但是在求解其大规模离散问题时，这些方法往往显得不适当，不充分――“捉襟见肘”。迭代法在数值计算中表现的特点，体现了它在求解这类问题时的卓越之处：计算过程中收敛快；矩阵不用被分割改变，甚至不用被表示，而仅以A和A^T矩阵-向量乘积运算的形式出现；采用原子运算，方便进行并行计算。这些优点都非常适合大规模离散问题的求解计算。当然“半收敛”现象阻碍了这种方法在实际计算中的应用，使得在实际得到的计算解不能很好的保证一种收敛到真实解的状态。本文的目的就是突破这种迭代型正则化方法的“半收敛”现象的限制，发展和改进迭代法在离散不适定反问题中的计算效果，并给出相应的杂交型正则化方法的形式。 |
| Other Abstract | Ill-posed inverse problems are widely used in a variety of scientific applications in modern times. Classical regularization methods are effective to compute a stable solution for this kind of problems, but many of these methods are inadequate or insufficient for solving large-scaled problems. The feature, which iterative methods characterize in numerical computing, reflects the advanced advantage for calculating these problems: fast convergence in computing; The matrix is never altered but only “touched” via the matrix-vector products with A and A^T atomic operations, which are simple to parallelize. All these advantages are very adequate to compute the solution for large-scaled problems. Still, the “semi-convergence” phenomenon obstructs these methods to be utilized in application, since computed solutions are not convergence to the true solution in general good way. This work addresses these limitations by developing and implementing the iterative regularization in order to get better computed solutions. |
| URL | 查看原文
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/224805
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| Collection | 数学与统计学院
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Recommended Citation
GB/T 7714 |
郑大威. 求解大规模线性离散不适定反问题的修正LSQR算法及其杂交型算法[D]. 兰州. 兰州大学,2011.
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