On regularized Hermitian splitting iteration methods for solving discretized almost‐isotropic spatial fractional diffusion equations
Zhong‐Zhi Bai, Kang‐Ya Lu · Numerical Linear Algebra with Applications · 2019
Summary The shifted finite‐difference discretization of the one‐dimensional almost‐isotropic spatial fractional diffusion equation results in a discrete linear system whose coefficient matrix is a sum of two diagonal‐times‐Toeplitz matrices. For this kind of linear systems, we propose a class of regularized Hermitian splitting iteration methods and prove its asymptotic convergence under mild conditions. For appropriate circulant‐based approximation to the corresponding regularized Hermitian splitting preconditioner, we demonstrate that the induced fast regularized Hermitian splitting preconditioner possesses a favorable preconditioning property. Numerical results show that, when used to precondition Krylov subspace iteration methods such as generalized minimal residual and biconjugate gradient stabilized methods, the fast preconditioner significantly outperforms several existing ones.