フィルタを用いた固有値問題の近似解法について

Abstract

We approximate eigenpairs of an eigenproblem whose eigenvalues are in a specified interval by using a filter. In this study, we assume the filter is a Chebyshev polynomial of a linear combination of resolvents. The filter is applied to a set of vectors to reduce the proportion of unwanted eigenvectors contained in the resulted set, so to make it spans a good approximation of the required invariant subspace. In general situations, a filter is applied to a random set of vectors, but before the original filter is applied if another filter with lower performance but requires less effort is applied to reduce the proportion of unwanted eigenvectors, the approximation of the invariant subspace can be improved, which we confirmed in our experiments.