期望解算子的稀疏压缩
Sparse Compression of Expected Solution Operators
摘要：
我们证明了随机系数的原型线性椭圆型微分算子的期望解算子可以用可计算的稀疏矩阵很好地逼近。这个结果是基于随机本地化的正交多分辨率分解的解决方案空间，允许稀疏近似反演的随机算子表示在这个基础上，以及其随机平均。近似期望解算子可以用经典的Haar小波来解释。当结合一个合适的抽样方法的期望，这种建设导致一个有效的方法来计算稀疏表示的预期解决方案运营商。
英文摘要：
We show that the expected solution operator of prototypical linear elliptic partial differential operators with random coefficients is well approximated by a computable sparse matrix. This result is based on a random localized orthogonal multiresolution decomposition of the solution space that allows both the sparse approximate inversion of the random operator represented in this basis as well as its stochastic averaging. The approximate expected solution operator can be interpreted in terms of classical Haar wavelets. When combined with a suitable sampling approach for the expectation, this construction leads to an efficient method for computing a sparse representation of the expected solution operator.
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