On row sequences of Padé and Hermite-Padé approximation

2015/02/13 by Lagomasino, Guillermo López
#30E10 #41A21 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.03958

Abstract

A survey of direct and inverse type results for row sequences of Padé and Hermite-Padé approximation is given. A conjecture is posed on an inverse type result for type II Hermite-Padé approximation when it is known that the sequence of common denominators of the approximating vector rational functions has a limit. Some inverse type results are proved for the so called incomplete Padé approximants which may lead to the proof of the conjecture and the connection is discussed.

Related

• Inverse results on row sequences of Hermite-Padé approximation
• Incomplete Padé approximation and convergence of row sequences of Hermite-Padé approximants
• Direct and inverse results on row sequences of simultaneous Padé-Faber approximants
• Inverse Theorem on Row Sequences of Linear Padé-orthogonal Approximation
• Higher order recurrences and row sequences of Hermite-Padé approximation