Boundary value methods for solving ordinary differential equations require the solution of non-symmetric, large and sparse linear systems. In this paper, we use the generalized minimal residual (GMRES) method to solve these systems. A circulant-block preconditioner is proposed to speed up the convergence rate of the GMRES method. Theoretical and practical arguments are given to show that this preconditioner is more efficient than some other circulant-type preconditioners in some cases.
1 Work supported by the research grant RG026/00-01S/JXQ/FST from University of Macau.
2 Joint work with Xiao-qing JIN and Vai-kuong SIN.