Summary: From an algebraic point of view, the expectation-maximization maximum likelihood (EMML) algorithm and image space reconstruction algorithm (ISRA) algorithms for positron emission tomography can be considered as iterative procedures for solving a class of systems of linear equations. We introduce an algorithm \(A(p)\), \(p\in\mathbb R\), such that \(A(1)\) coincides with EMML and \(A(-1)\) with a version of ISRA. Some examples illustrate the speed of convergence. Applications are indicated to: (i) the Bernstein-Bézier representation; (ii) the B-spline interpolation; (iii) the inverse problem for Markov chains; (iv) the problem of finding the stationary distribution of a regular Markov chain.