In this chapter we give two possible algorithms related to the recursive computation of elements in a Padé table for a fls. The successive approximants have the same numerator degree but the denominator degree increases as we proceed. This means that we move from left to right on a horizontal line in the Padé table. The algorithms are well known methods for the solution of Toeplitz systems [TRE1], [ZOH1] and are related to the methods of Levinson and Schur known in digital filtering theory. Much information on these algorithms and many related ones can be found in a thesis by D.R.Sweet [SWE].