Journal of Computational Physics ( IF 4.1 ) Pub Date : 2021-08-24 , DOI: 10.1016/j.jcp.2021.110654 Jordi Feliu-Fabà , Lexing Ying
This paper introduces a factorization for the inverse of discrete Fourier integral operators of size that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a hierarchical matrix representation is constructed for the hermitian matrix arising from composing the Fourier integral operator with its adjoint. This representation is inverted efficiently with a new algorithm based on the hierarchical interpolative factorization. By combining these two factorizations, an approximate inverse factorization for the Fourier integral operator is obtained as a product of sparse matrices with entries. The resulting approximate inverse factorization can be used as a direct solver or as a preconditioner. Numerical examples on 1D and 2D Fourier integral operators, including a generalized Radon transform, demonstrate the performance of this new approach.
中文翻译:
离散傅立叶积分算子的近似求逆
本文介绍了大小离散傅立叶积分算子的逆因式分解 可以应用于准线性时间。分解首先用蝴蝶分解逼近算子。接下来,为由傅立叶积分算子与其伴随组合而产生的厄密矩阵构造分层矩阵表示。使用基于分层插值分解的新算法可以有效地反转这种表示。通过结合这两种分解,傅立叶积分算子的近似逆分解可以作为 稀疏矩阵 条目。得到的近似逆分解可用作直接求解器或预处理器。一维和二维傅里叶积分算子的数值示例,包括广义 Radon 变换,证明了这种新方法的性能。