学术报告：Fast Algorithms for Block Triangular Toeplitz Matrix with
Applications to Time-Fractional Partial Differential Equations
报告人：孙海卫教授 （澳门大学）
报告时间：5月30日下午5:00-6:00
报告地点：数学院433
摘要：A fast approximate inversion method is proposed for the block lower triangular Toeplitz
with tri-diagonal blocks (BL3TB) matrix. The BL3TB matrix is approximated by a block
circulant-like matrix, which can be efficiently inverted using the fast Fourier transforms.
The good approximation is proved under a certain condition. As applications, the
discretized matrix by a finite difference method for the fractional sub-diffusion equation
is shown as a BL3TB matrix and satisfies this condition. Therefore, the proposed method
can be efficiently applied to find the numerical solution of the fractional sub-diffusion
equation. For the block lower triangular Toeplitz-like with tri-diagonal blocks (BL3TB-
like) matrix, we propose a direct method based on the divided-and-conquer strategy with
cheaper computational complexity. Numerical experiments are carried out to
demonstrate the excellence performance of the proposed methods.
