COMPUTING MATRIX-VALUED NEVANLINNA-PICK INTERPOLATION

We describe a computational method, known as the Nevanlinna algorithm, for the matrix-valued Nevanlinna-Pick interpolation. The original int erpolation problem formulated using the Caratheodory class of matrix-v alued rational functions is first converted to an equivalent setting u sing the Schur class of rational functions. As a result, the necessary and sufficient Pick's condition for the interpolation becomes consist ent with the scalar-valued formulation, so that some efficient techniq ues developed for the scalar-valued interpolation can be employed or m odified for the matrix-valued case. We give a brief, yet sufficiently clear, derivation and a detailed arithmetic complexity analysis for th e algorithm. We show that an n-point matrix-valued Nevanlinna-Pick int erpolation using the new algorithm requires approximately 95nm3 comple x arithmetic operations, where m is the matrix dimension.