Matrix Padé approximation of rational functions (Q1373132)

This paper on rectangular matrix valued Padé approximation discusses existence and uniqueness issues of left and right approximants as well as certain minimality conditions on the degrees in numerator and denominator matrix polynomials of the approximants. The ``simplest'' approximants corresponds to ``smallest possible degrees'' in numerator and denominator. However, depending on the definition of the degrees, different conclusions can be drawn. These results are based on a detailed investigation of ranks of block Hankel matrices. For example, one of the main results describes rank conditions to decide whether a given matrix series corresponds to a matrix rational function. All the rank information can be collected in tables and from these tables it is then relatively easy to derive the corresponding properties for the approximants.