Details
| Original language | English |
|---|---|
| Pages (from-to) | 191-219 |
| Number of pages | 29 |
| Journal | Linear Algebra and Its Applications |
| Volume | 173 |
| Issue number | C |
| Publication status | Published - Aug 1992 |
Abstract
A unified and self-contained approach to the block structure of Shank's table and its cross rules is presented. Wynn's regular and Cordellier's singular cross rules are derived by the Schur-complement method in a unified manner without appealing to Padé approximation. Moreover, by extending the definition of Shank's transformation to certain biinfinite sequences and by introducing a parameter it is possible to get more consistency with respect to Möbius transformations. It is well known that Padé approximants in general don't have this property.
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Discrete Mathematics and Combinatorics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Linear Algebra and Its Applications, Vol. 173, No. C, 08.1992, p. 191-219.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Shank's transformation revisited
AU - Beckermann, B.
AU - Neuber, A.
AU - Mühlbach, G.
PY - 1992/8
Y1 - 1992/8
N2 - A unified and self-contained approach to the block structure of Shank's table and its cross rules is presented. Wynn's regular and Cordellier's singular cross rules are derived by the Schur-complement method in a unified manner without appealing to Padé approximation. Moreover, by extending the definition of Shank's transformation to certain biinfinite sequences and by introducing a parameter it is possible to get more consistency with respect to Möbius transformations. It is well known that Padé approximants in general don't have this property.
AB - A unified and self-contained approach to the block structure of Shank's table and its cross rules is presented. Wynn's regular and Cordellier's singular cross rules are derived by the Schur-complement method in a unified manner without appealing to Padé approximation. Moreover, by extending the definition of Shank's transformation to certain biinfinite sequences and by introducing a parameter it is possible to get more consistency with respect to Möbius transformations. It is well known that Padé approximants in general don't have this property.
UR - http://www.scopus.com/inward/record.url?scp=44049112136&partnerID=8YFLogxK
U2 - 10.1016/0024-3795(92)90429-E
DO - 10.1016/0024-3795(92)90429-E
M3 - Article
AN - SCOPUS:44049112136
VL - 173
SP - 191
EP - 219
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
IS - C
ER -