Access the full text.
Sign up today, get DeepDyve free for 14 days.
A. Sidi, W. Ford, David Smith (1986)
Acceleration of convergence of vector sequencesSIAM Journal on Numerical Analysis, 23
A. Sidi (2008)
A de Montessus type convergence study of a least-squares vector-valued rational interpolation procedureJ. Approx. Theory, 155
A. Sidi (2004)
A new approach to vector-valued rational interpolationJ. Approx. Theory, 130
A. Sidi (1990)
Quantitative and constructive aspects of the generalized Koenig's and de Montessus's theorems for Pade´ approximantsJournal of Computational and Applied Mathematics, 29
P. Graves-Morris, E. Saff, R. Varga (1985)
Rational Approximation and Interpolation
A Sidi (2003)
Cambridge Monographs on Applied and Computational Mathematics 10
M. Golomb (1943)
Zeros and poles of functions defined by Taylor seriesBulletin of the American Mathematical Society, 49
A. Householder (1970)
The numerical treatment of a single nonlinear equation
J. Stoer, R. Bulirsch (2002)
Introduction to Numerical Analysis
P. Graves-Morris, E. Saff (1984)
A de montessus theorem for vector valued rational interpolants
A. Sidi (2017)
A de Montessus type convergence study for a vector-valued rational interpolation procedureIsrael Journal of Mathematics, 163
R deMontessus de Ballore (1902)
Sur les fractions continue algébriquesBull. Soc. Math. France, 30
E. Saff (1972)
An extension of Montessus de Ballore's theorem on the convergence of interpolating rational functionsJournal of Approximation Theory, 6
M Golomb (1943)
Zeros and poles of functions defined by power seriesBull. Amer. Math. Soc., 49
A. Sidi (2006)
Algebraic properties of some new vector-valued rational interpolantsJ. Approx. Theory, 141
J L Walsh (1960)
American Mathematical Society Colloquium Publications, Volume 20
P. Graves-Morris, E. Saff (1988)
Row convergence theorems for generalised inverse vector-valued Pade´ approximantsJournal of Computational and Applied Mathematics, 23
A. Sidi (2003)
Practical Extrapolation Methods: Preface
Scientifiques L’É.N.S, S. Pincherle
Sur les fractions continues algébriquesAnnales Scientifiques De L Ecole Normale Superieure, 6
J. König (1884)
Ueber eine Eigenschaft der PotenzreihenMathematische Annalen, 23
P. Graves-Morris, E. Saff (1991)
Divergence of vector-valued rational interpolants to meromorphic functionsRocky Mountain Journal of Mathematics, 21
W. Gragg, A. Householder (1966)
On a theorem of KoenigNumerische Mathematik, 8
W B Gragg, A S Householder (1966)
On a theorem of KönigNumer. Math., 8
K. Atkinson (1979)
An introduction to numerical analysis
P. Davis (1965)
Interpolation and approximation
A. Sidi (1994)
Rational Approximations from Power Series of Vector-Valued Meromorphic FunctionsJournal of Approximation Theory, 77
P. Graves-Morris, E. Saff (1991)
An extension of a row convergence theorem for vector Pade´ approximantsJournal of Computational and Applied Mathematics, 34
We continue our study of convergence of IMPE, one of the vector-valued rational interpolation procedures proposed by the author in a recent paper, in the context of vector-valued meromorphic functions with simple poles. So far, this study has been carried out in the presence of corresponding residues that are mutually orthogonal. In the present work, we continue to study IMPE in the same context, but in the presence of corresponding residues that are not necessarily orthogonal. Choosing the interpolation points appropriately, we derive de Montessus type convergence results for the interpolants and König type results for the poles and residues.
Computational Methods and Function Theory – Springer Journals
Published: Feb 6, 2010
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.