Regular algebras of dimension 2, the generalized eigenvalue problem and Padé interpolation

DOI

10.2991/jnmp.2005.12.s2.23How to use a DOI?

Abstract

We consider the generalized eigenvalue problem A = B for two operators A, B. Self-similar closure of this problem under a simplest Darboux transformation gives rise to two possible types of regular algebras of dimension 2 with generators A, B. Realiztion of the operators A, B by tri-diagonal operators leads to a theory of biorthogonal rational functions. We find the general solution of this problem in terms of the odinary and basic hypergeometric functions. In special cases we obtain general Padé interpolation tables for the exponential and power function on uniform and exponetial grids.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Alexei Zhedanov
PY  - 2005
DA  - 2005/12/01
TI  - Regular algebras of dimension 2, the generalized eigenvalue problem and Padé interpolation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 333
EP  - 356
VL  - 12
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s2.23
DO  - 10.2991/jnmp.2005.12.s2.23
ID  - Zhedanov2005
ER  -