Minimal vector Padé approximation

摘要

We describe the minimal vector Padé approximation problem, which consists in finding Padé approximants with a common denominator for a number of series. These approximants are minimal in the sense that for a given order of approximation and a given discrepancy in numerator and denominator degrees, the degree of the rational approximant is minimal. Properties and solution methods are derived from an associated partial realization problem.