Journal of Nonlinear Mathematical Physics

Volume 12, Issue Supplement 2, December 2005, Pages 333 - 356

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

Authors
Alexei ZHEDANOV
Corresponding Author
Alexei ZHEDANOV
Available Online 2 December 2006.
DOI
https://doi.org/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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - 100
Pages
333 - 356
Publication Date
2006/12
ISBN
91-974824-5-5
ISSN
1402-9251
DOI
https://doi.org/10.2991/jnmp.2005.12.s2.23How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Alexei ZHEDANOV
PY  - 2006
DA  - 2006/12
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  - 1402-9251
UR  - https://doi.org/10.2991/jnmp.2005.12.s2.23
DO  - https://doi.org/10.2991/jnmp.2005.12.s2.23
ID  - ZHEDANOV2006
ER  -