Spectral Power Iterations for the Random Eigenvalue Problem
Spectral Power Iterations for the Random Eigenvalue Problem
复制标题
随机特征值问题的谱功率迭代
DOI：
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复制
发表时间：
2014
期刊：
影响因子：
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通讯作者：
R. Ghanem
中科院分区：
文献类型：
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作者：
H. Meidani;R. Ghanem
针对随机特征值问题，提出了两种计算效率较高的算法。提出了一种基于幂迭代技术的主导特征对的计算方法。然后将该算法扩展到寻找其他次优随机特征对。算子中的不确定性用多项式混沌展开来表示，随机本征值和特征向量也考虑了类似的表示。这些算法的不同之处在于它们收敛到真正的随机特征对的速度以及它们估计指定数量的次优特征对的能力。通过两个算例对算法进行了验证，所得结果与精确解和蒙特卡罗抽样合成的解基本一致。
Two computationally efficient algorithms are developed for solving the stochastic eigenvalue problem. An algorithm based on the power iteration technique is proposed for the calculation of the dominant eigenpairs. This algorithm is then extended to find other subdominant random eigenpairs. The uncertainty in the operator is represented by a polynomial chaos expansion, and a similar representation is considered for the random eigenvalues and eigenvectors. The algorithms are distinguished due to their speed in converging to the true random eigenpairs and their ability to estimate a prescribed number of subdominant eigenpairs. The algorithms are demonstrated on two examples with close agreement observed with the exact solution and a solution synthesized through Monte Carlo sampling.
DOI：
10.1137/140999359
发表时间：
2016
期刊：
SIAM/ASA Journal on Uncertainty Quantification
影响因子：
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作者：
Sousedík, Bedřich;Elman, Howard C.
通讯作者：
Elman, Howard C.