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Block preconditioning for the conjugate gradient method. (English) Zbl 0556.65022

Different block preconditionings for the conjugate gradient methods are investigated for solving positive definite block tridiagonal systems. These preconditionings are based on different sparse approximate matrix inverses. The proposed methods are compared with other well-known preconditionings as for example the point incomplete Cholesky factorization, by testing them on discretizations of two dimensional boundary value problems for elliptic partial differential equations.
Reviewer: V.Mehrmann

MSC:

65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65F50 Computational methods for sparse matrices
35J25 Boundary value problems for second-order elliptic equations
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