Toeplitz-like preconditioners for the solution of block Toeplitz systems
Fu‐Rong Lin · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
We study the solution of block system Tm,nx equals b by preconditioned conjugate gradient methods where Tm,n is an m X m block Toeplitz matrix with n X n Toeplitz blocks. This kind of systems occur in a variety of applications, such as the 2D digital signal processing and the discretization of 2D partial differential equations. We propose a new preconditioner for this kind of block systems. Our preconditioner is defined as the sum of block Toeplitz matrix with Toeplitz blocks and three sparse matrices with structure. Our numerical tests show that our preconditioner is superior to Level-1 and Level-2 circulant preconditioners.