Bidiagonal Decompositions and Accurate Computations for the Ballot Table and the Fibonacci Matrix

ABSTRACT Riordan arrays include many important examples of matrices. Here we consider the ballot table and the Fibonacci matrix. For finite truncations of these Riordan arrays, we obtain bidiagonal decompositions. Using them, algorithms to solve key linear algebra problems for ballot tables and Fibonacci matrices with high relative accuracy are derived. We include numerical experiments showing the accuracy of our method.