A parallel algorithm based on Galerkin theory for block-tridiagonal linear systems

The work presented in this paper focuses on parallel iterative method for solving block-tridiagonal linear systems. Being based on Galerkin theory predetermining Wm = Vm, and forming a suitable matrix Vm, a parallel iterative method on distributed-memory multi-computer is established. Then Eq. (3.1)-(3.3) are provided for carrying out computation required by our parallel algorithm. Furthermore, convergence is proved when the coefficient matrix A is a symmetric positive definite matrix, and the sufficient condition is given. In the end, two illustrative examples implemented on HP rx2600 cluster show that our algorithm's parallel acceleration rates and efficiency are higher.