Section: New Results
Rational and meromorphic approximation
Participant : Laurent Baratchart.
This work has been done in collaboration with Herbert Stahl (TFH Berlin) and Maxim Yattselev (Univ. Oregon at Eugene, USA).
We completed and published this year the proof of an important result in
approximation theory, namely the counting measure of
poles of best
This result warrants source recovery techniques used in section 6.1.1 .
We also studied partial realizations, or equivalently Padé approximants to transfer functions with branchpoints. Identification techniques based on partial realizations of a stable infinite-dimensional transfer function are known to often provide unstable models, but the question as to whether this is due to noise or to intrinsic instability was not clear. In the case of 4 branchpoints, expressing the computation of Padé approximants in terms of the solution to a Riemann-Hilbert problem on the Riemann surface of the function, we proved that the pole behaviour generically shows deterministic chaos [49] .