On projectively contraction mapping method (Q1382582)

In the real Hilbert space \(\mathcal H\) a bounded linear operator \(A\:\mathcal H\to \mathcal H\) is considered moreover the equation \[ A\psi = 0\tag{1} \] has a unique solution with precission up to the multiplication by \(-1\). It is assumed that \[ \| I - A\| _{\mathcal H^\bot} < 1. \] In the paper a sequence \(\{\varphi_n\}\) is constructed which converges to the solution \(\psi\) of equation (1) with respect to the norm of space \(\mathcal H\).