A connection of series approximations and the basis of the Krylov space in block algorithms of Coppersmith and Montgomery

In this paper, some properties of the Wiedemann–Coppersmith algorithm are studied. In particular, when the matrix of a linear system is symmetric, an orthogonal basis of the Krylov space is constructed with the help of approximations of formal series from odd steps of this algorithm. We propose some modifications that use the described properties.