[For the entire collection see Zbl 0538.00036.]
An algorithm for the computation of the singular value decomposition of a real \(m\times n\)-matrix A is presented. It is essentially the power method for \(A^ TA\) and \(AA^ T\). The iterates are orthogonalized against the singular vectors already found. The numerical properties are analysed and an acceleration method in the case of clusters of singular values is given. Here the relation to the usual subspace iteration is not discussed. It is shown that this method is superior to the Golub-Kahan- algorithm if only few singular values and vectors are required, if the multiplication \(A\cdot x\) and \(A^ T\cdot x\) is cheap and if good initial guesses are available. This is true in many applications, e.g. in adaptive state space realization. Many numerical experiments are reported.