\input zb-basic
\input zb-ioport
\iteman{io-port 01472875}
\itemau{Abramov, A.A.; Yukhno, L.F.}
\itemti{An elimination method for linear problems.}
\itemso{Comput. Math. Math. Phys. 38, No.4, 527-535 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No.4, 547-556 (1998).}
\itemab
The authors consider the elimination problem for general linear equations in Hilbert spaces. The method suggested for solving this problem is based on the ideas of conjugate direction method. This method allows a given linear functional of a solution to be computed without evaluating the solution itself. The authors prove the convergence of this method and investigate the character of this convergence in some cases when the original linear problem is ill-posed.
\itemrv{Alexey Tret'yakov (Siedlce)}
\itemcc{}
\itemut{linear equations; elimination method; ill-posed; convergence; conjugate direction method}
\itemli{}
\end