BTTB preconditioners for BTTB systems (Q415342)

The authors analyze the BTTB system \(T_{m,n}[f]\mathbf{x}=\mathbf{b}\) by the preconditioned conjugate gradient (PCG)method, where \( T_{m,n}[f]\) denotes the \( m \times n\) block Toeplitz matix with \(n \times n\) Toeplitz blocks (BTTB) generated by a \(( 2\pi, 2\pi)\) - periodic continuous function \(f(x,y)\). Numerical results show that the propose BTTB preconditioner is more efficient than block circulant preconditioners.