Circulant-block preconditioners for solving ordinary differential equations.
Solving linear initial value problems of ordinary differential equations by boundary value methods requires the solution of non-symmetric, large and sparse linear systems. A circulant-block preconditoner for the generalized minimal residual method is proposed to solve these systems. The operation costs and the convergence rate are investigated. The proposed preconditioner is compared with \textit{D. Bertaccini}'s [SIAM J. Sci. Comput. 22, No. 3, 767--786 (2000; Zbl 0976.65071)] -- and strong-type block-circulant -- preconditioners and a block-circulant-circulant-block preconditioner. The two numerical experiments show the advantage of the new preconditioner.
scientific article; zbMATH DE number 1978092