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**Asynchronous two-stage iterative methods.**
*(English)*
Zbl 0821.65010

A system of linear algebraic equations with a square nonsingular matrix is studied. The matrix is supposed to be partitioned into blocks in such a manner that the blocks be square.

One investigates the standard block Jacobi method and also three algorithms of a block two-stage iterative method two of which are asynchronous. The main attention is paid to those conditions under which the asynchronous two-stage iterative methods are convergent. The convergence of asynchronous two-stage iterative methods is proved for matrices with special properties, namely, for monotonic matrices and for \(H\)-matrices.

The asynchronous two-stage processes are analysed from the point of view of the volume of computational work on each iteration, also of usage of information obtained on the previous iteration with processors, as well as the confirmity of parallelizing of computations on parallel computers.

One investigates the standard block Jacobi method and also three algorithms of a block two-stage iterative method two of which are asynchronous. The main attention is paid to those conditions under which the asynchronous two-stage iterative methods are convergent. The convergence of asynchronous two-stage iterative methods is proved for matrices with special properties, namely, for monotonic matrices and for \(H\)-matrices.

The asynchronous two-stage processes are analysed from the point of view of the volume of computational work on each iteration, also of usage of information obtained on the previous iteration with processors, as well as the confirmity of parallelizing of computations on parallel computers.

Reviewer: I.N.Molchanov (Kiev)