Fast estimation of continuous Karhunen-Loeve eigenfunctions using wavelets
Fast estimation of continuous Karhunen-Loeve eigenfunctions using wavelets
复制标题
使用小波快速估计连续 Karhunen-Loeve 特征函数
DOI：
10.1109/78.972484
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
K. Amaratunga
中科院分区：
文献类型：
--
作者：
J. Castrillón;K. Amaratunga
本文提出了一种快速估计连续Karhunen-Loeve特征函数的小波方法。通过将系综函数投影到正交或双正交插值函数空间，改进了快拍法。在良好的分段光滑多项式集成函数下，所产生的协方差矩阵的大小大大减小，而不会牺牲太多的精度。此外，协方差矩阵C/spl tilde/可以被容易地分解，使得C/spl tilde/ = A/sup T/ A，并且因此，可以应用更稳定的奇异值分解（SVD）算法。一个插值方案，减少了计算投影到双正交子空间上的系综函数到一个单一的样本。此外，通过将系综函数投影到小波空间上，协方差矩阵可以通过多分辨率分解来稀疏化。稀疏和非稀疏协方差矩阵之间的特征值的误差界也来自。
This paper develops a new wavelet method for the fast estimation of continuous Karhunen-Loeve eigenfunctions. The method of snapshots is modified by projecting the ensemble functions onto orthogonal or biorthogonal interpolating function spaces. Under well-behaved piecewise smooth polynomial ensemble functions, the size of the covariance matrix produced is greatly reduced, without sacrificing much accuracy. Moreover, the covariance matrix C/spl tilde/ may be easily decomposed such that C/spl tilde/ = A/sup T/ A, and thus, the more stable singular value decomposition (SVD) algorithm may be applied. An interpolating scheme that reduces the computation of projecting the ensemble functions onto the biorthogonal subspace to a single sample is also developed. Furthermore, by projecting the ensemble functions onto wavelet spaces, the covariance matrix may be sparsified by a multiresolution decomposition. Error bounds for the eigenvalues between the sparsified and nonsparsified covariance matrix are also derived.