A note on the matrix valued q-d algorithm and matrix orthogonal polynomials on [0,1] and [0,∞)

In this note a matrix version of the q-d algorithm is introduced. It is shown that the algorithm may be used to obtain the coefficients of the recurrence relations for matrix orthogonal polynomials on the interval [0,∞) and [0,1] from its moment generating functional. The algorithm is illustrated by several examples, which generalize classical orthogonal polynomials on the real line.