Volume 12, Issue Supplement 2, December 2005, Pages 333 - 356
Regular algebras of dimension 2, the generalized eigenvalue problem and Padé interpolation
Available Online 1 December 2005.
- https://doi.org/10.2991/jnmp.2005.12.s2.23How to use a DOI?
- 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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Cite this article
TY - JOUR AU - Alexei ZHEDANOV PY - 2005 DA - 2005/12 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 - 1776-0852 UR - https://doi.org/10.2991/jnmp.2005.12.s2.23 DO - https://doi.org/10.2991/jnmp.2005.12.s2.23 ID - ZHEDANOV2005 ER -