@Article{EAJAM-12-2,
author = {Yao-Ning, Liu and V., Muratova, Galina},
title = {A Block Fast Regularized Hermitian Splitting Preconditioner for Two-Dimensional Discretized Almost Isotropic Spatial Fractional Diffusion Equations},
journal = {East Asian Journal on Applied Mathematics},
year = {2022},
volume = {12},
number = {2},
pages = {213--232},
abstract = {<p style="text-align: justify;">Block fast regularized Hermitian splitting preconditioners for matrices arising
in approximate solution of two-dimensional almost-isotropic spatial fractional diffusion
equations are constructed. The matrices under consideration can be represented as the
sum of two terms, each of which is a nonnegative diagonal matrix multiplied by a block
Toeplitz matrix having a special structure. We prove that excluding a small number
of outliers, the eigenvalues of the preconditioned matrix are located in a complex disk
of radius $r&lt;1$ and centered at the point $z_0=1$. Numerical experiments show that
such structured preconditioners can significantly improve computational efficiency of
the Krylov subspace iteration methods such as the generalized minimal residual and
bi-conjugate gradient stabilized methods. Moreover, if the corresponding equation is
almost isotropic, the methods constructed outperform many other existing preconditioners.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.070621.300821},
url = {https://global-sci.com/article/82463/a-block-fast-regularized-hermitian-splitting-preconditioner-for-two-dimensional-discretized-almost-isotropic-spatial-fractional-diffusion-equations}
}