Problems and progress in vector Pade approximation

[摘要] Some open problems in vector Pade approximation are stated, and some recent de Montessus-type theorems governing convergence of rows of the vector Pade table are contrasted. We show how these results indicate when it is more appropriate to use generalised inverse vector Pade approximants or their hybridised form. We show how a straightforward analogue of the Berlekamp-Massey algorithm may be used to calculate generalised inverse vector Pade approximants. This algorithm is applied to the derivation of a new low-order hybrid vector approximant. Related results include the case of a row convergence theorem for a complex-valued power series using a Clifford inverse instead of the Moore-Penrose inverse.

[发布日期] 1997-01-13

[效力级别]  Proceedings Paper

[关键词] vector Pade;approximant;vector-valued power series;de Montessus theorem;vector epsilon algorithm;Berlekamp-Massey algorithm;Clifford algebra;pfaffian