A multipurpose computing device includes a solver receiving a working matrix and an initial matrix corresponding to a system of equations and residual data; and an adapter receiving the initial matrix as well as a filtering matrix and calculates a working matrix corresponding to an equation system solved by the solver. The working matrix checks a stability condition with the initial matrix, comprising a comparison of two matrix products including the filtering matrix or the transpose thereof, and the initial matrix and the working matrix, respectively. The adapter renumbers the initial matrix and the filtering matrix in order to produce a modified matrix and a modified filtering matrix using an ordering rule that is a function of a dependency condition, and recursively calculates the working matrix representation with these matrices. The solver works recursively on the working matrix to provide a solution without inverting the initial matrix.