(1) Due to a coding mistake the algorithm used to solve the test problems in Sections 1.10.7.2 and 1.10.7.3 of Part I (see Acta Numerica 1994) was not a genuine conjugate gradient algorithm. Indeed, the search direction sequence {wn}n≥0 was improperly defined leading to a slow convergence; for the ‘small’ values of k (e.g. 102, 103) the computed results were essentially correct, but for larger values the slow convergence prevented us from reaching the correct limit since we stopped iterating after a fixed number of iterations (300 or 500, depending of the test problem).