Birecursive interpolation algorithm: a formalism for solving systems of linear equations

This paper presents a simple unifying algorithm for iterative methodsthat use two Krylov subspaces. This new approach leads us to ageneral algorithm called the bi-recursive interpolation algorithm (Bi-RIA), which is a generalization of the recursif interpolation algorithm (RIA), the Bi-RIA includes the iterative methods of Lanczos type usingtwo auxilary vectors. We will show how to choose two free sets of parametersand one matrix in the Bi-RIA for recovering known iterativemethods of Lanczos type. Other choices of these parameters yield somenew methods.