Recursive interpolation algorithm: a formalism for solving systems of linear equations—I. Direct methods

This paper presents a simple unifying algorithm for solving systems of linear equations. Solving a system of linear equations will be interpreted as an interpolation problem. This new approach leads us to a general algorithm called the recursive interpolation algorithm ria, which includes the direct methods and some of the iterative methods. A version of the ria with pivoting strategy will be given. We will also show how to choose two free sets of parameters in the ria for recovering known direct methods. Other choices of these parameters yield some new methods.