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Multigrid and conjugate gradient methods as convergence acceleration techniques. (English) Zbl 0577.65086
Multigrid methods for integral and differential equations, Workshop Bristol/Engl. 1983, Inst. Math. Appl. Conf. Ser., New Ser. 3, 117-167 (1985).
Authors’ summary: Multigrid and conjugate gradient type techniques for the acceleration of iterative methods are discussed. A detailed discussion is given of incomplete factorizations. The theoretical background of the classical conjugate gradient method and preconditioning is briefly reviewed. A conjugate gradient type method for non-symmetric positive definite systems is presented. Mulitgrid methods are discussed, and two portable, autonomous computer codes are introduced. Multigrid treatment of convection-diffusion entails special difficulties, and ways to overcome these are outlined. Numerical experiments on a set of test problems are reported. Efficiency and robustness of several conjugate gradient and multigrid methods are compared and discussed.
Reviewer: S.F.McCormick

65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations