title: |
Regular algebras of dimension 2, the generalized eigenvalue problem and Padé interpolation |
|
publication: |
||
| volume-issue: | 12 - Supplement 2 | |
| pages: | 333 - 356 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2005.12.s2.23 (how to use a DOI) | |
author(s): |
Alexei ZHEDANOV |
|
publication date: |
December 2005 |
|
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: |
©
Atlantis Press. This is an open-access article distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
|
full text: |