Lots of linear algebra problems can be reduced to the resolution of a linear system: A.X = B. When they are expressed in such a form, it appears that A often admits a pattern : it is said to be a structured matrix. To accelerate its resolution, one can take advantage of that structure. This talk will present our efficient implementation of the Morf-Bitmead-Anderson algorithm for the inversion of scalar structured matrices : its time complexity is quasi-linear in the size of A. That implementation has been associated with a Newton Iteration taking advantage of the structure of A : it is able to inverse polynomial structured matrices with again a time complexity quasi-linear in the size of A.