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High performance preconditioning. (English) Zbl 0693.65027
The paper deals with the parallel solution of linear algebraic systems with special matrices arising from the discretization of elliptic partial differential equations. To solve the resulting algebraic systems preconditioned conjugate gradient methods are considered. The role of the preconditioner is to reduce the number of iteration steps in parallel implementation. The methods proposed are well suited for supercomputers possessing vector facilities. The approaches presented are compared by solving the three-dimensional problem of the size 34$$\times 34\times 34$$ on a CYBER-205 vector machine.
Reviewer: M.Vajteršic

##### MSC:
 65F10 Iterative numerical methods for linear systems 65F35 Numerical computation of matrix norms, conditioning, scaling 65Y05 Parallel numerical computation 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations
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