No. 9 (00077)

Family name : Moiseenko
Given name : Vladimir
Affiliation : Institute of Plasma Physics, National Science Center
              "Kharkov 
Institute of Physics and Technology", 61108 Kharkov, Ukraine
Abbreviation : IPP NSC KhIPT
E-mail address : moiseenk@ipp.kharkov.ua
Title : Modified Generalized Minimum Residual Method
Authors : V.E.Moiseenko
Abstract : 
The Generalized Minimum Residual Method (GMRes) is the effective tool
for approximate solving a large linear system with non-Hermitian matrix.
The main part of its algorithm contains a loop inside which a new vector
of the basis in the Krylov subspace is generated and a new row of the
matrix of the minimization problem is calculated. The problem is that
until finishing the cycle, the approximate solution is not known. There
is the only estimate for the norm of the residual that could be used to
judge if the required accuracy is attained.

The proposed version of GMRes has the same numerical cost and returns
the same result. However, its algorithm is different. Each step of the
internal cycle it generates a new approximation for the solution. The
true norm of residual is also computed each step using the simple
recursive formula that does not contain any matrix-vector or inner
product computations.