Fast algorithms for Nevanlinna-Pick interpolation and H∞ optimization

Fast algorithms are derived for the scalar and tangential directional Nevanlinna-Pick interpolation problems. These fast algorithms require fewer multiplications than standard algorithms for these problems. The scalar interpolation problem, which arises in SISO (single input single output) H∞ optimization, is solved using a three-term recurrence similar to that of the so-called split algorithms for linear prediction. The tangential directional interpolation problem, which arises in MIMO (multiple input multiple output) H∞ optimization, is solved using an algorithm similar to a series of Householder transformations. Applications to H∞ optimization are noted