Circulant-block preconditioners for solving ordinary differential equations

Authors:
Xiao-qing Jin;Vai-kuong Sin;Li-li Song
Affiliations:
Faculty of Science and Technology, University of Macau, C. Postal 3001, Macau;Faculty of Science and Technology, University of Macau, C. Postal 3001, Macau;Faculty of Science and Technology, University of Macau, C. Postal 3001, Macau
Venue:
Applied Mathematics and Computation
Year:
2003

Citing 6
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Abstract

Boundary value methods for solving ordinary differential equations require the solution of non-symmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. 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. A class of waveform relaxation methods is also proposed to solve the linear systems.