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**Row projection methods for large nonsymmetric linear systems.**
*(English)*
Zbl 0752.65024

The paper deals with conjugate gradient accelerated row projection methods for nonsymmetric linear systems and their comparison with other nonsymmetric solvers. One of them is based on Kaczmarcz’s method, another one on Cimmino’s method and a new one is introduced which involves fewer matrix-vector operations, explicitly reduces the problem size and is error-reducing in the two-norm.

It is verified both theoretically and numerically that these methods are more robust than other solvers and successfully solve large systems (of size 13824 and 216000) with indefinite real parts and eigenvalues arbitrarily distributed in the complex plane. The most important contribution is a guideline for choosing the row partititioning so that the angles between the corresponding subspaces are large, actually without having to compute them.

It is verified both theoretically and numerically that these methods are more robust than other solvers and successfully solve large systems (of size 13824 and 216000) with indefinite real parts and eigenvalues arbitrarily distributed in the complex plane. The most important contribution is a guideline for choosing the row partititioning so that the angles between the corresponding subspaces are large, actually without having to compute them.

Reviewer: P.Polcar (Brno)

### MSC:

65F10 | Iterative numerical methods for linear systems |