Brakhage's implicit iteration method and the information complexity of equations with operators having closed range

An a posteriori stopping rule connected with monitoring the norm of the sec ond residual is introduced for Brakhage's implicit nonstationary iteration method, applied to ill-posed problems involving linear operators with close d range, It is also shown that for some classes of equations with such oper ators, the algorithm consisting in combination of Brakhage's method with so me new discretization scheme is order optimal in the sense of information-b ased complexity. (C) 1999 Academic Press.