2017/06/12 by Harri Hakula, Hakula, Harri, Mikael Laaksonen +1
Computer Science · Mathematics · #65C20 #65N12 #65N15 #65N25 #65N30 #FOS: Mathematics #Mathematical Approximation and Integration #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1706.03558
openalex publication_date 2017/06/12 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We consider and analyze applying a spectral inverse iteration algorithm and\nits subspace iteration variant for computing eigenpairs of an elliptic operator\nwith random coefficients. With these iterative algorithms the solution is\nsought from a finite dimensional space formed as the tensor product of the\napproximation space for the underlying stochastic function space, and the\napproximation space for the underlying spatial function space. Sparse\npolynomial approximation is employed to obtain the first one, while classical\nfinite elements are employed to obtain the latter. An error analysis is\npresented for the asymptotic convergence of the spectral inverse iteration to\nthe smallest eigenvalue and the associated eigenvector of the problem. A series\nof detailed numerical experiments supports the conclusions of this analysis.\nNumerical experiments are also presented for the spectral subspace iteration,\nand convergence of the algorithm is observed in an example case, where the\neigenvalues cross within the parameter space. The outputs of both algorithms\nare verified by comparing to solutions obtained by a sparse stochastic\ncollocation method.\n